PHYSICS KINEMATICS
Learning Objectives:
♦ Rest and motion, kinds of motion.
♦ We will investigate the words used to describe the motion of objects. The hope is to gain
a comfortable foundation with the language that is used throughout the study of mechanics.
We will study the terms such as scalars, vectors, distance, displacement, speed, velocity
and acceleration.
♦ How to describe straight-line motion in terms of average velocity, instantaneous velocity,
average acceleration and instantaneous acceleration etc.
♦ How to solve problems involving straight-line motion with uniform acceleration.
Real time application:
What distance must an airliner travel down a runway before reaching takeoff speed?
When you throw a baseball straight up in the air, how high does it go? When a glass slips
from your hand, how much time do you have to catch it before it hits the floor? This kind
of all questions are answered.
Usefull to sketch the time tables for buses, trains, etc.
Usefull in Engineering works.
Usefull in finding height of a building, height of a bridge from water level etc.
Without motion there will be no vehicle, no river, no wind can flow etc i.e. we can not expect
our life without these.
Important formulae:
1. Distance travelled
Speed = ---------------
Time taken
2. Average speed = total distance / total time.
3. If a body travels first half of the distance with a speed V1 and second half of the distance
with a speed V2 then average speed is given by
Vavg = 2V1V2 / (V1 + V2)
4. If v1 and v2 are the speeds of a body during the first half and second half times then
average speed = (v1 + v2) / 2.
5. If a body travels first 1/3 rd of the distance with a speed V1 and next 1/3 rd of the distance
with a speed V2 and remaining 1/3 rd of the distance with a speed V3 then the average
speed is given by
V = 3v1v2v3 / (v1v2 + v2v3 + v3v1)
6. Displacement
Velocity (V) = -----------
time
7. Average Velocity = total displacement / total time.
8. Acceleration = (v - u) / t = change in velocity / time.
9. V = u + at
10. s = ut + 1/2 at²
11. v² - u² = 2as
Mechanics:
The branch of physics which deals with the study of forces, motion and their
relationship is called Mechanics.
The study of mechanics is divided into three parts.
i) Statics:
The branch of mechanics which deals with objects at rest is called statics.
ii) Kinematics:
The branch of mechanics which deals with the motion of objects without
considering the cause of motion is called kinematics.
iii) Dynamics:
The branch of mechanics which deals with the cause of motion is called
dynamics.
Rest and Motion:
Rest: A body is said to be at rest if it does not change it’s position with respect to
surroundings.
Eg: A book on a table.
Motion: A body is said to be in motion if it changes it’s position with time with respect to
surroundings.
Eg: a moving car with respect to earth frame.
Rest and Motion are relative:
Absolute = Something that does not depend on anything else.
Relative = Something that is dependent on other things.
Whenever we express the state of a body to be at rest or in motion, we are expressing
the state with respect to (in relation to) some other body which we identify as the frame of
reference.
Kinds of Motion:
Based on different classification we define the following
1) Translatory Motion
The motion of an object is said to be translatory if the position of the object is changing
with respect to a fixed point or object. All the particles of a body executing translatory
motion move in the same direction traversing parallel paths.
Eg: A car moving in a straight line.
2) Rotatory Motion
The motion of an object is said to be rotatory if the motion of all the particles of body is
circular (i.e. along a circular path) with respect to an imaginary line called the axis of
rotation. This happens when an object spins. The axis of rotation may be internal or
external to the body.
The center of the circular path that each particle traces lies on the “axis of rotation”.
Eg: 1) A spinning Top
2) The Wheel of a moving vehicle
3) The hands of a clock
3) Oscillatory Motion
Oscillatory motion is repetitive and fluctuates between two locations. The to and fro motion of
an object about a fixed point is called oscillatory motion.
Eg: 1) An Oscillating Table Fan
2) The Pendulum of a wall clock
3) A Swinging Cradle
4) Opening and Closing the door of a refrigerator.
4) Circular Motion
A motion in which the body traverses a circular path is called circular motion. This is a
kind of translatory motion where the body reaches the initial position each time it
completes traversing the circle.
Eg: Each particle of a body executing rotatory motion executes circular motion.
5) Periodic Motion
Any Motion that repeats itself at regular intervals of time is called periodic motion.
Eg: 1) A bouncing ball
2) A Vibrating spring
3) Every body executing circular motion can be said to be executing periodic motion
4) Every body executing oscillatory motion can be said to be executing periodic motion.
6) Random Motion
Irregular Motion of bodies changing the nature of motion frequently is called Random
Motion.
Eg: 1) Motion of Football player on the ground.
2) Motion of house flies.
7) One dimensional motion: If just one coordinate is sufficient to specify the position of
the particle completely then its motion is called one dimensional motion.
8) Two dimensional motion: If two coordinates are sufficient to specify the position of
the particle completely then its motion is called two dimensional motion.
9) Three dimensional motion: If three coordinates are sufficient to specify the position
of the particle completely then its motion is called dimensional motion
Scalars:
The physical quantities which have only magnitude but not direction are called scalars.
Ex: Mass, length, distance, time, area, volume, density, work etc.
Vectors:
The physical quantities which have both magnitude and direction are called vectors.
Ex: Displacement, velocity, acceleration, force etc.
Distance:
The length of the curve along which the body moves is called a distance. It is scalar
quantity.
Units: cm (In C.G.S. System); m (In S.I. System)
Displacement:
The shortest pathlength between the initial and final positions of a body is called
displacement. It is a vector quantity.
Examples 1:
Suppose a bus starting from station A travels 15000 m to reach station B then the distance
covered by the bus is 15000 m. Now if the bus returns to the station A then distance covered
is 15000 m and the total distance covered by the bus during the trip from A to B and then back
to A from B is 15000 m + 15000 m = 30000 m.
But the displacement when the bus moves from A to B and then from B to A is zero.
Examples 2:
Suppose a person moves 3 meters from A to B and 4 meters from B to C as shown in the
figure. The total distance traveled by him is 7 meters and he is displaced only by 5 m which
is the shortest distance between his initial position and final position.
Examples 3:
Now let us consider an object changing its position, with respect to a fixed point called the
origin 0. xi and xf are the initial position and final position of the object. Then the displacement
of the object = xf – xi.
Case 1
Suppose the object is moving from +1 to +4, then displacement = xf – xi = +4 – (+1) = +3
Case 2
If the object is moving from -3 to -1 then displacement = xf – xi = –1 – (–3)= 2
Case 3
If the object is moving from +5 to +2 then displacement = xf – xi = +2 – (+5) = –3.
Case 4
If the object follows the path as shown in the figure then the final position and the initial
position is the same i.e., the displacement is zero.
Getting Direction:
On the Earth the directions parallel to the ground which are assumed to be flat are called as horizontal directions. North, East, West & south directions are
horizontal and they are represented on paper as in side figure. The direction exactly midway
between N and E is called NE. Similarly NW, SW & SE. If the directions don't fall exactly
midway then they won't be represented as NE, NW, SE, SW & SE. They are represented as
in the following example.
Example-1:
The direction represented in the given figure is
Sol:
30 due N of E or 60 due E of N
Example-2:
An athlete completes one round of a circular track of radius R in 40 s. What will be his
displacement at the end of 2 min 20 s?
Sol:
The time = 2 min 20s = 140s
In 40 seconds athlete completes = 1 round
In 140 seconds athlete will completes
= 140/40 round = 3.5 rounds
The displacement in 3 rounds = 0
So net displacement = 2R
Example-3:
If an object turns through an angle θ along a circular path of radius r from point A to point B
then
i) distance d = rθ
ii) displacement 2x = 2r sin(θ/2)
Example-4:
A horse is tied to a rope of length 5 m and the other end of the rope is tied to a pole. find the
displacement and the distance travelled by the horse in the following cases.
i) When the horse makes half revolution along a circular path.
ii) When it makes one full revolution
iii) when it makes 3/4 th of the revolution
sol: i) Half revolution along the circular path.
Distance travelled by the horse = 2πr / 2 = πr = π×5 = 5π m.
Displacement of the horse = diameter of the circular path, 10 m from H1 to H2
ii) When the horse makes full revolution
Distance travelled by the horse = circumference of the circular path
= 2πr = 2π×5 = 10π m
Displacement of the horse = zero
iii) When the horse makes 3/4 th of the revolution
Distance travelled by the horse = 3/4 th of the circumference of the circle
= 3/4 (2πr) = 3/2 π × 5 = 15/2 π = 7.5π m.
Displacement of the horse = shortest distance between H1 and H2
= √(5² + 5²) = √50 = 5√2 m along H1 to H2
Single correct answer questions:
1. A student walks 1kilometer due east and 1kilometer due south. Then she runs 2
kilometers due west. The magnitude of the student's resultant displacement is
A) 3.4 km B) 1.4 km C) 4km D) 0 km
2. If a person could fly nonstop around the equator of the earth and reaches back at initial
point then displacement of person is ...
A) 2π radius of the earth B) 2π square of radius of the earth
C) diameter of earth D) 0
3. A person walks 3m towards east and then 4m towards north. Find the displacement of the
person.
A) 5m B) 10m C) 15m D) 7m
4. A boy walks 12m towards west and then 5m towards south. Find the displacement of the
boy.
A) 17m B) 13 m C) 8m D) 12m
5. A car travels 10km towards south and then 24km towards east. Find the displacement of
the car.
A)15m B) 9m C) 34m D) 26m
6. A train travels 60km towards north and then 80km towards west. Find the displacement
of the car.
A) 180km B) 100km C) 240km D) 208km
7. Statement of a scalar just consists of its magnitude along with a proper algebraic sign.
Among the following the quantity which is not a scalar?
A) 20 kg B) 15 m C) 40 s D) 13 m due north
8. Among the following the quantity which one is a scalar?
A) 18m due west B) 20 m due south C) 30 m D) 23 m due north
9. Mohini walks 100m towards west then turns and walks back the way she came 20m.
What distance she travelled? What is her displacement?
A) 80m, 120m B) 120m, 80m C) 120m,100m D) 100m, 120m
10. An Olympic runner is running totally 1600m circle track during a race. What are the distance and displacement he covered?
A) 1600m, 0m. B)40m,1600m C) 6400m,0m D) 1600m,64m
11. A shopper walks forward 20 m turns right and walks 5 m then turns left and walks in the
original direction 10m there after turns left again for 5m. What is the distance she covered? What is her displacement?
A) 20m, 10m B) 30m, 20m C) 30m,40m D) 40m, 30m
12. Some hikers travel 2 km north turns toward the west and travel 4km turns towards the
south and travel 6 km then finally travel east for 4 km. What is their distance? What is
their displacement
A) 5m,20m B) 10m, 8m C) 16m, 4km D) 4m, 16m
Multi correct answer questions:
13. Rakesh drives his bike 7 kilometer north. He stops for lunch and then drives 5 kilometer
east. Then choose the correct
a) Totally he covered a distance of 12 km
b) his displacement is 8.6 km
c) finally he travelling towards west
A) Only a, b B) Only b, c C) Only a, c D) all a, b, c
14. Abdul walks to the pizza place for lunch. He walks 1 km east then 1 km south and then 1
km east again. Then choose the correct
a) Toally he covered a distance of 3 km
b) His displacement is 5 km
c) his displacement after travelling 1 km south is 2 km
A) Only a, b B) Only b, c C) Only a, c D) all a, b, c
Fill in the blanks:
15. A person starts from his house to office and is back again to his house.Then the displacement is...........
16. A person moves 3 m due north then turns towards east and moves again 4 m.The displacement of person is............
17. An object is moving round in a circular path. It completes one revolution and goes back to
its starting point. The ________ is zero but the ________ travelled is the circumference
of the circular path.
Match the following:
18. A person is running in the circular path of radius 'r' then
Column - I
a) after one complete revolution
b) after half revolution
c) after one fourth revolution
d) after three by fourth of revolution
Column - II
1) distance = 2πr, displacement = 0
2) distance = πr, displacement = 2r
3) distance = πr/2, displacement = 2r
4) distance = 3πr/2, displacement = 2r
A) a-1, b-2, c-3, d-4
B) a-1, b-2, c-4, d-2
C) a-2, b-1, c-3, d-4
D) a-1, b-3, c-2, d-4
Comprehension type questions:
19. An athlete running in a circular track of radius 70 m. Calculate his distance and
displacement for
a) one revolution b) two revolutions c) half revolution
d) one fourth revolution e) three by fourth revolution.
Solve the following:
20. On his fishing trip Justin takes the boat 12km south. The fish aren’t biting so he goes 4km
west. He follows a school of fish 1km north. What distance did he cover? What was his
displacement?
21. Preston goes on a camel safari in Africa. He travels 5km north then 3 km east and then 1km north
again. What distance did he cover? What was his displacement?
22. Naresh travels 8 m east then 4 m north. What distance did he cover? What was his displacement?
Higher order thinking skills (HOTS):
23. Stephen buys a new moped. He travels 3 km south and then 4 km east. How far does he
need to go to get back to where he started in a shortest way?
24. A man is facing south. He turns 1350 in the anti clock wise direction and then 1800 in
clockwise direction. Which direction is he facing now?
25. An athlete completes one round of a circular track of radius R in 40 sec. What will be his
displacement at the end of 2 min.20 sec?
26. A body moves from one corner of an equilateral triangle of side 10 cm to the same corner
along the sides.Then the distance and displacement are respectively?
27. A body is moving along the circumference of a circle of radius ‘R’ and completes half of
the revolution.The ratio of its displacement to distance is?
Teaching Task:
1) A 2) D 3) A 4) B 5) D 6) B 7) D 8) C 9) B 10) A 11) D
12) C 13) A 14) D 15) zero 16) 5 m 17) displacement, distance 18) A
19) a) 440 m, 0 m b) 880 m, 0 m c) 220 m, 140 m d) 110 m, 140 m e) 330 m,
140 m 20) 11.6 m 21) 9 km, 6.7 km 22) 8.94 m 23) 5 km
24) SE 25) 2R 26) 30 cm, 0 cm 27) 2:π
Speed:
The distance travelled by the body in unit time is called its speed.
Speed (V) = distance travelled / time taken
* speed is a scalar quantity.
* it is represented by v or u
units: CGS Unit: cm/s, SI unit: m/s,
Uniform speed: If a body travels equal distances in equal intervals of time then it is said to
be moving with uniform speed.
Eg: motion of ball on a frictionless plane surface.
Non - uniform speed: If a body travels unequal distances in equal intervals of
time (or) equal distance in unequal intervals of time the body is said to be travelling with
non uniform (or) variable speed.
Instantaneous speed: The speed of a body at any instant known as the instantaneous
speed. speedometer of vehicle measures the instantaneous speed.
Velocity: The rate of displacement (or) displacement per unit time is called velocity.
Velocity = displacement / time
* velocity is a vector quantity.
units: CGS Unit: cm/s, SI unit: m/s,
Note:
* The velocity of a body can be zero, negative or positive.
* The numerical value of velocity of a body can be equal to speed only if the body is moving
along a straight line in the same direction.
* The velocity of a body can never be greater than the speed of that body.
Uniform velocity:
If a body travels equal displacements in equal intervals of time then the body is said to be
travelling with uniform velocity.
Non - uniform (or) variable velocity:
If a body covers unequal displacements in equal intervals of time then it is said to be
travelling with variable velocity.
Single correct answer questions:
1. A body moves with a speed of 36 km/h. What is its speed in m/s.
A) 10 m/s B) 20 m/s C) 30 m/s D) 40 m/s
2. A man moves with a speed of 15 m/s. Express his speed in km/hr.
A) 34 km/h B) 54 km/h C) 36 km/h D) 18 km/h
3. An athlete runs in a circular path of radius 14 m, 10 times in 10 minutes. Calculate the
speed.
A)1.6 m/s B) 1.26 m/s C)1.36 m/s D) 1.46 m/s
4. The train ‘A’ travelled a distance of 120 km in 3 hours whereas another train ‘B’ travelled a
distance of 180 km in 4 hours. Which train travelled faster?
A) train A B) both trains C) train B D) none
5. Calculate the distance travelled by a car moving with a speed 35 km/h in 12 minutes.
A) 15 km B) 7 km C) 14 km D) 9km
6. Imagine two boys Ramu and Somu running a 300 m race. Let as imagine that Ramu
finishes the race in 15 sec and somu finishes 30sec. Who run faster?
A) Ramu B) somu C) equal speed D) nonE
Multiple option type:
7. A scooterist covers a distance of 3 kilometers in 5 minutes. This speed equal to
a) 1000 cm/s b) 10 m/s c) 36 km/h
A) a, b only correct B) a, c only correct C) b, c only correct D) all a, b, c correct
8. Ahmed is moving in his car with a velocity of 45 km/h. Then he will cover a distance of
a) 45 km in one hour b) 750 m in one minute c) 12.5 m in one sec
A) a, b only correct B) a, c only correct C) b, c only correct D) all a, b, c correct
Fill in the blanks:
9. 1 km/h = .............................. m/s.
10. The speedometer of a vehicle measures ...........................
11. 15 m/s = ......................... km/h
12. 1 m/s = ............................... cm/s.
13. 1 km/min = ...................... m/s.
Match the following:
14. A body moving in circular path of radius 7 m completes half rotation in 2 sec, then its
a) distance traveled
b) displacement
c) speed
d) velocity
1) 11 m/s
2) 22m
3) 7 m/s
4) 14 m
A) a - 1, b - 2, c - 3, d - 4
B) a - 4, b - 3, c - 1, d - 2
C) a - 1, b - 4, c - 3, d - 2
D) a - 2, b - 4, c - 1, d - 3
Comprehension type:
15. In a wall clock length of seconds arm is 7 cm, minutes arm is 5 cm, hours arm is 3.5 cm
i) speed of seconds arm is
A) 11/15 cm/s B) 7/5 cm/s C) 10/7 cm/s D) none
ii) Speed of minutes arm is
A) 11/15 cm/s B) 11/378 cm/s C) 11/180 cm/s D) none
iii) Speed of hours arm is
A) 11/15 cm/s B) 11/378 cm/s C) 11/21600 cm/s D) none
Solve the following:
16. A Randy Johnson fastball is thrown with a velocity of 41.5 m/s, How long does it take the
ball to reach the plate that is 18.44 meters from the pitcher's mound?
17. A bicyclist has an average velocity of 35 km/hr. How far will she travel in 6 hrs?
18. How long will it take you to complete a 135 mile trip if your velocity is 45 mph?
Higher order thinking skills (HOTS):
19. A car covers a distance of 600 m in 2 minutes whereas a train covers a distance
of 75 km in 50 minutes. Find the ratio of their speed
A) 1 : 5 B) 5 : 1 C) 1 : 2 D) 2 : 1
20. A bus covers a certain distance in 60 minutes if it runs at a speed of 60 km/hr. What must
be the speed of the bus in order to reduce the time of journey by 40 minutes?
A) 90 kmph B) 80 km/h C) 70 km/h D) 60 km/h
21. A person crosses a 600cm long bridge in 5cmin. What is his speed in kmph?
A) 7.2 B) 6 C) 5 D) 4.5
22. How far would you travel moving at 12m/s for 3min?
A) 160 m B) 2160m C) 612 m D) 123 m
Acceleration:
The change in velocity per unit time (OR) The rate of change of velocity of a body is called Acceleration.
Acceleration = change velocity / time
Units: m/s² (S.I system), cm/s² (C.G.S system)
The velocity of the car increases continuously with respect to time says that
the car accelerates. The increase in velocity per unit time is called acceleration.
The velocity of the car decreases continuously with respect to time says that the car
decelerates or retards.
The decrease in velocity per unit time is called deceleration or retardation.
Negative acceleration is called Retardation or Deceleration.
Accelerations are of two types:
i) Positive acceleration: If body’s velocity increases gradually then it said to possesses
positive acceleration.
Example: A freely falling body.
ii) Negative acceleration (or) Deceleration (or) Retardation:
If body’s velocity decreases gradually then it said to possesses retardation.
Ex: A vertically projected body.
Equations of motion:
The relation between v, u, a and s for a body moving with uniform acceleration in a straight
path are well known to us. Equations which relate these quantities are known as equations of motion.
The equations of motion are
i) V = u + at where u → Initial Velocity
ii) s = ut + 1/2 at²
iii) v² - u² = 2as
v → Final Velocity
t → time
a → uniform acceleration
S → Distance travelled
Example-8:
If a sports car at rest accelerates uniformly to a speed of 144 km h-1 in 5 s then find
distance travelled by it?
Sol:
u = 0, v = 144 km h-1 = 40 m s-1, t = 5 s
a = (v - u) / t = 8 m s-2
s = 1/2 × 8 × (5)² = 100 m
Example-9:
The driver of a car moving with a velocity of 54 km h-1 applies brakes to decrease its
velocity to 36 km h-1. If the retardation produced by the brakes is 2 m s-2, arrange the
following steps in a sequential order to calculate the distance travelled by the car.
Sol:
u = 54 km h-1 = 15 m s-1, v = 36 km h-1 = 10 m s-1, a = -2.0 m s-1
Using v² - u² = 2as => s = (v² - u²) / (2a)
=> s = (100 - 225) / -2a
=> s = 125 / 4 = 31.25 m
Example-10:
A bike starting from rest picks up a velocity of 72 km h-1 over a distance of 40m. Calculate
its acceleration.
Sol: Given, u = 0, v = 72 km h-1 = 20 m s-1, s = 40m
using v² - u² = 2as => (20)² - 0 = 2a x 40 => a = 400 / 80 = 5 m s-2
Example-11:
A car moving along a straight road with a speed of 72 km h-1 is brought to rest within 3 s
after the application of brakes. Calculate the deceleration produced by the brakes.
Sol:
Initial velocity ‘u’ = 72 km h-1 = 20 m s-1
Final velocity, v = 0 m s-1,
(v - u) / t = a => deceleration = 20 / 3 = 6.67 m s-2
Choose the correct answer:
1. A train starting initially with a speed of 36 km/h picks up a velocity of 108 km/h in
half minute. Calculate its acceleration in m/s².
A) 0.66 m/s² B) 0.76 m/s² C) 0.86 m/s² D) 0.96 m/s²
2. A motor cyclist has 8sec to stop his motor cycle which is travelling at 50 km/h. What is
his retardation?
A) 1.4 m/s² B) 1.74 m/s² C) 1.04 m/s² D) 2.74 m/s²
3. A scooter acquires a velocity of 36 km/h in 10seconds just after the start. Calculate
the acceleration of the scooter.
A) 7m/s² B) 4m/s² C) 3m/s² D) 1m/s²
4. A bus increases its speed from 36km/h to 72km/h in 10seconds. Calculate its
acceleration.
A) 7m/s² B) 4m/s² C) 3m/s² D) 1m/s²
5. If a Ferrari with an initial velocity of 10 m/s accelerates at a rate of 50 ms-2 for 3 s, what will
be its final velocity?
A) 150m/s B) 100 m/s C) 120 m/s D) 160 m/s
6. Josh rolled a bowling ball down a lane in 2.5 s. The ball traveled at a constant acceleration
of 1.8 m/s² down the lane and was traveling at a speed of 7.6 m/s by the time it reached
the pins at the end of the lane. How fast was the ball going when it left Tim’s hand?
A) 1.2 m/s B) 3 m/s C) 3.1 m/s D) 4.1 m/s
7. An aeroplane accelerates down on a runway at 3.20 m/s² for 32.8 s until is finally lifts off
the ground. Determine the distance traveled before takeoff.
A) 1720m B) 1270m C) 1050m D) 1500m
8. A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.
A) 6.4m/s² B) 7.1m/s² C) 8.1 m/s² D) 7.4m/s²
9. A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine
the acceleration of the car and the distance traveled.
A) 73.8m B) 79.8m C) 98.7m D) 89.7m
10. Rocket-powered sleds are used to test the human response to acceleration. If a rocket-
powered sled is accelerated to a speed of 444 m/s in 1.83 seconds then what is the
acceleration and distance that the sled travel?
A) 406m B) 306m C) 206m D) 604m
Multiple option type:
11. A body starting from rest and moving with uniform acceleration of 5 m/s². Then choose
the correct
a) its initial velocity is zero
b) its velocity will increase with time
c) its velocity at the end of 5 sec is 25 m/s
d) its velocity at the end of 10 sec is 250 m/s
A) only a, b, c B) only b, c, d C) only a, c, d D) all a, b, c, d
12. A person running at 20 m/s speeds up to 60 m/s in 4 seconds. Then choose the correct
a) his initial velocity is 20 m/s b) his final velocity is 60 m/s
c) his acceleration is 10 m/s² d) his velocity will be 120 km/h in next 6 sec
A) only a, b, c B) only b, c, d C) only a, c, d D) all a, b, c, d
Fill in the blanks:
13. The velocity of the body decreasing gradually is said to be in...................
14. The S.I unit of deceleration is ....................
15. Another name for deceleration is.....................
Match the following:
16. Column A
a) u = 10m/s, v = 0m/s, t = 1s
b) u = 5m/s, v = 5m/s, t = 5s
c) u = 0m/s, v = 10m/s, t = 5s
d) u = 2m/s, v = 1m/s, t = 2s
Column B
1) a = 2m/s²
2) a = -10m/s²
3) a = -0.5m/s²
4) a = 0m/s²
Comprehension type:
17. Acceleration is ratio between change in velocity and time
i) The velocity of car changes from 18 km/h to 72 km/h in 30 s the acceleration in km/h² is
A) 648 B) 6480 C) 64800 D) 648000
ii) The change in velocity of motor bike is 54 km/h in one minute the acceleration in km/h² is
A) 324 B) 3240 C) 32400 D) 324000
iii) A speeding car changes its velocity from 108 km/h to 36 km/h in 4s the deceleration in m/s².
A) 6 B) 5 C) 4 D) 3
Solve the following:
18. A bullet is moving at a speed of 367 m/s when it embeds into a lump of moist clay. The
bullet penetrates for a distance of 0.0621 m. Determine the acceleration of the bullet
while moving into the clay. (Assume a uniform acceleration.)
19. A stone is dropped into a deep well and is heard to hit the water 3.41 s after being dropped.
Determine the depth of the well.
20. A plane has a takeoff speed of 88.3 m/s and requires 1365 m to reach that speed. Determine
the acceleration of the plane and the time required to reach this speed.
Higher order thinking skills (HOTS):
21. A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m.
Determine the acceleration of the bike.
A) 0.8m/s² B) 7.1m/s² C) 0.712 m/s² D) 7.4m/s²
22. An engineer is designing the runway for an airport. Of the planes that will use the airport,
the lowest acceleration rate is likely to be 3 m/s². The takeoff speed for this plane will be
65 m/s. Assuming this minimum acceleration and what is the minimum allowed length
for the runway?
A) 738m B) 798m C) 987m D) 704m
Researchers:
1. What statement best describes the given figure? [NSO-2011]
A) The earth is rotating around the sun B) The sun is rotating around the Earth
C) The Earth is revolving around the sun D) The sun is revolving around the Earth
2. In circular motion the, .......... [NSO-2014]
A) direction of motion is fixed B) direction of motion changes continuously
C) velocity constant D) none
3. Consider the motion of the tip of the minute hand of clock. In one hour. [NSO-2014]
A) The distance covered zero B) the displacement is zero
C) the average speed is zero D) none
4. Which of the following is example of vibratory motion? [NSO-2009]
A) a car moving along a circular track B) a freely falling stone
C) motion of the string of violin D) motion of the planet around the sun
5. Which of the following is example of periodic motion? [NSO-2008]
A) A car taking a turn on a curved road B) A crane filing over a water pond
C) A lift moving down D) march past of soldiers
6. A passenger in a moving train is at ....... w.r.t ground and is at ....... with other passenger in
same train. [NSO-2009]
A) Motion,motion B) rest,rest C) motion, rest D) rest, motion
7. If a body travels half the distance with velocity v1 and the next half with velocity v2,
average velocity will be given by. [NSO-2008]
Vavg = (2v1v2) / (v1 + v2)
8. An artificial satellite is moving in circular orbit of 4225.km. find its speed if it takes 24hr to
revolve around the earth. [NSO-2012]
A) 30.7km/s B) 5.67km/s C) 6.14km/s D) 1.57km/s
9. The length of a square field is 6 m. Parul ran 6 rounds around the field. The total distance that she covered, is ........ [NSO-2008]
A) 216 m B) 144 m C) 176 m D) 186 m
10. Two simple pendulums P and Q are given. P completes 20 oscillations in 32 sec and Q
completes 30 oscillations in 45 sec. Which pendulum is faster? [NSO-2008]
A) P B) Q C) both have same time period D) data insufficiently
11. Two boys P and Q are running along the same path. P is 10 m ahead of Q initially. However,
Q catches up with P. after running 50 m. Assuming that both boys are running at a constant speed. What is the ratio of the speeds of P and Q? [NSO-2014]
A) 6 : 5 B) 5 : 6 C) 4 : 1 D) 4 : 5
12. Sonic vibrations were sent down from a return after 2 seconds. What is the depth of the sea.
If the speed of sound in water is 1.5 kms-1 ? [NSO-2012]
A) 150 m B) 3 m C) 1.5 m D) 750 m
13. A car driver took a total of two hours to make a journey of 75 km. He had a coffee break
of half an hour and spend a quarter of an hour stationary in a traffic jam. What was his
average speed during the journey? [NSO-2012]
A) 38 kms-1 B) 50 kms-1 C) 60 kms-1 D) 75 kms-1
14. Talking one light year equal to 9.4 X 10^15 m and one day equal to 86400 s, what will be the
speed of light in light year per day if the speed of light in ms-1 is 3 X 10^8 ? [NSO-2012]
A) 2.75 X 10-3 ly day-1 B) 3.75 X 10-3 ly day-1
C) 2.75 X 10^3 ly day-1 D) 3.75 X 10-3 ly day-1
15. The ultrasonic waves take 4 second to travel from the ship to the bottom of the sea and
back to the ship (in the form of an echo). What is the depth of the sea? [NSO-2009]
A) 3000 m B) 2000 m C) 1000 m D) 500 m
16. A taxi driver noted reading on the odometer fitted in vehicle as 1050 km, when he started
the journey. After 30 minutes drive, he noted that the odometer reading was 1086 km.
What is the average speed of the taxi? [NSO-2009]
A) 20 m/s B) 25 m/s C) 30 m/s D) 40
17. How long does it take for the earth to rotate on its axis seven times? [NSO-2010]
A) One day B) One week C) One month D) One year
Key
Teaching Task:
1) A 2) B 3) D 4) C 5) B 6) A 7) D 8) D 9) 5/18
10) instantaneous speed 11) 54 12) 100 13) 50/3 14) D
15) i) A ii) B iii) C 16) 0.444sec 17) 210km 18) 3hr 19) A 20) A
21) A 22) B
Learner’s Task
Beginners (Level - I)
1. The numerical ratio of average velocity and average speed.
A) always less than one B) always equal to one
C) always more than one D) equal or less than one
2. An ant covers 2cm, 1.5cm, 2.5cm, 3cm in one second each. Find average speed of it.....
A) 3m/s B) 2.5 m/s C) 1.5m/s D) none
3. A car covers 40km in 1 hr and then 10 km in 15min then car moving with
A) variable speed B) uniform speed C) average speed D) none
4. 36kmph =...... m/min
A) 10 B) 129.6 C) 600 D) 100
5. A cyclist moving in circular path of radius 200m covers half revolution in 5min. its average speed is......m/s
A) 44/21 B) 4/3 C) 88/7 D) 2/3
6. The magnitude of average velocity is equal to average speed when a particle moves
A) in a curved path B) in the same direction
C) with constant speed D) with constant speed
7. A car completes one lap around a circular track of radius 50 meters. The time it takes to
complete the lap is 1.2 minutes. What is the total distance covered?
A) 4.66m/s B) 4.26m/s C) 4.36m/s D)3.36m/s
8. In the above question what is the average speed of the car in meters per second?
A) 0.694 B) 0.56 C) 0.51 D)0.88
9. A family leaves from New York City and is flying to Los Angles which is 2800miles away.
It takes 3.25 hours to fly from New York to O’Hare International Airport in Chicago IL.
There they have a one hour layover and fly to Los Angles in 2.75 hours. What is the
average speed of the whole travel?
A) 30 mph B) 40 mph C) 50 mph D) 60 mph
10. A car travels 300.0 m East then 400.0 m West. If it takes 18.0 seconds to do this.
what is the car’s average speed and average velocity?
A) 38.18 m/s, 5.55m/s B) 38.88 m/s, 5.55m/s
C) 38.88 m/s, 5.05m/s D) 30.88 m/s, 5.55m/s
11. A runner runs for 1.00 hour at an average speed of 2.00 m/s. How far does she run during this time?
A) 120m B) 12m C) 1.20m D) Both a&c
12. A car travels a distance of 30 miles for 2 hrs and 45 miles for next 3 hrs. Calculate its average speed.
A) 15mph B) 1.5mph C) 5mph D) 10mph
13. A body moves 30 m at a uniform speed of 20 m/s and next 30 m at a uniform speed of 12 m/s. Calculate its average speed.
A) 15 m/s B) 12 m/s C) 10 m/s D) 20m/s
14. A car covers 30 km at a uniform speed of 60 km/h and the next 30 km at a uniform speed of 40 km/h. Find the total time taken and the average speed?
A) 70 minutes, 48 km/h B) 75 minutes, 48 km/h
C) 75 minutes, 40 km/h D) 25 minutes, 48 km/h
15. A train travels some distance with a speed of 30 km/h and returns with a speed of 45 km/h. Calculate the average speed of the train.
A) 36 km/h B) 18 km/h C) 56 km/h D) 24 km/h
16. Sam is driving along the highway towards Saint John. He travels 150km in 3.00hrs. What
is his average speed for his trip?
A) 50 km/h B) 18 km/h
C) 56 km/h D) 24 km/h
17. A vehicle travels 2345 m [W] in 315 s towards the evening sun. What is its average velocity? (7.4 m/s [W])
A) 8m/s B) 7.4 m/s C) 8m/s D) 6m/s
Solve the following:
1. Hari is practicing for a running race. For 1st 1/2 hour he runs 0.25 miles and for the next 1/2 hour he runs for 0.2 miles. Calculate the average speed?
2. A car moves from A to B at a speed of 50 km/hr and comes back from B to A at a speed of 30 km/hr. Find its average speed during the journey.
3. A car covers a distance of 60 km in 3 hours. However, for the first 40 km it travels 16 km/hr. At what speed must it travel for the rest of the distance in order to complete the journey on time?
4. Calculate the average velocity at a particular time interval of a particle if it is moves 5 m at 2 s and 15 m at 4s along x-axis?
Multiple option type:
1. Consider the motion of the tip of the minute hand of a clock. In one hour
a) The displacement is zero b) The distance covered is zero
c) average speed is zero d) average velocity is zero.
A) only a,b correct B) only a,c correct
C) only a, d correct D) all a, b, c, d correct
2. When a body completes certain journey, then choose the correct
a) its distance can be zero b) its displacement can be zero
c) its average speed can be zero d) its average velocity can be zero
A) only a, b B) only a, c C) only b, c D) only b, d
3. When a body moves form one place to another place, choose the correct
a) its distance can be equal to or greater than displacement
b) its average speed can be equal to or greater than average velocity
A) only a B) only b C) both a, b D) both are wrong
Fill in the blanks:
4. Car moving on circular track its average velocity after one round......
5. The ratio of total displacement to the total interval of time of a body is ......called
6. The ratio of the total distance travelled to the total time of travel is called ......
7. SI unit of average speed or average velocity is ......................
8. If average speed is zero then average velocity is ...........................
Match the following:
1. A car is running in a circular track of radius R, and takes a time T to complete each 1/4 th of the distance.
a) after one rotation average speed is
b) after one rotation average velocity is
c) after half rotation average velocity is
d) after 1/4 th rotation average velocity is
1) zero
2) πR / 2T
3) √2 R / T
4) R / T
A) a-2, b-1, c-4, d-3
B) a-1, b-2, c-3, d-4
C) a-4, b-3, c-2, d-1
D) a-2, b-3, c-4, d-1
2. If a body covers the first x % of the total time with velocity v1 and the remaining
(100 - x) % of the time with velocity v2, then
a] If x = 20
b] If x = 30
c] If x = 40
d] If x = 50
1) Vavg = (v1 + v2) / 2
2) Vavg = (4v1 + 6v2) / 10
3) Vavg = (3v1 + 7v2) / 10
4) Vavg = (2v1 + 8v2) / 10
A) a-1, b-2, c-3, d-4
B) a-2, b-1, c-4, d-3
C) a-4, b-3, c-2, d-1
D) a-4, b-3, c-1, d-2
Comprehension type:
1. If a particle moves along a straight line distance of 29 m in time of 5 sec and a distance
55 m in time of 14 sec. Then
i) Total distance traveled by the particle
A) 29 m B) 55 m C) 84 m D) 14 m
ii) Total time taken by the particle is
A) 5 sec B) 14 sec C) 19 sec D) 29 sec.
iii) The average velocity of a particle is
A) 2.89 m/sec B) 4.42 m/s C) 9.82 m/s D) zero
2. Mr. Bean travelled 240 km in 4 hours by train and then travelled 120 km in 3 hours
by car and 3 km in 1/2 hour by cycle. Then
i) Speed of train is
A) 20 kmph B) 40 kmph C) 60 kmph D) 80 kmph
ii) Speed of car is
A) 20 kmph B) 40 kmph C) 60 kmph D) 80 kmph
iii) Speed of bicycle is
A) 6 kmph B) 8 kmph C) 10 kmph D) 12 kmph
iv) Total distance travelled by Mr. Bean is
A) 240 km B) 120 km C) 3 km D) 363 km
v) Mr. Bean travelled for a total time of
A) 3.5 hr B) 5.5 hr C) 7.5 hr D) 9.5 hr
vi) Average speed of Mr. Bean for the total trip is
A) 48.4 km/hr B) 52.3 km/h C) 56.7 km/h D) zero
Acceleration:
The change in velocity per unit time (OR) The rate of change of velocity of a body is called Acceleration.
Acceleration = change velocity / time
Units: m/s² (S.I system), cm/s² (C.G.S system)
The velocity of the car increases continuously with respect to time says that
the car accelerates. The increase in velocity per unit time is called acceleration.
The velocity of the car decreases continuously with respect to time says that the car
decelerates or retards.
The decrease in velocity per unit time is called deceleration or retardation.
Negative acceleration is called Retardation or Deceleration.
Accelerations are of two types:
i) Positive acceleration: If body’s velocity increases gradually then it said to possesses
positive acceleration.
Example: A freely falling body.
ii) Negative acceleration (or) Deceleration (or) Retardation:
If body’s velocity decreases gradually then it said to possesses retardation.
Ex: A vertically projected body.
Equations of motion:
The relation between v, u, a and s for a body moving with uniform acceleration in a straight
path are well known to us. Equations which relate these quantities are known as equations of motion.
The equations of motion are
i) V = u + at where u → Initial Velocity
ii) s = ut + 1/2 at²
iii) v² - u² = 2as
v → Final Velocity
t → time
a → uniform acceleration
S → Distance travelled
Example-8:
If a sports car at rest accelerates uniformly to a speed of 144 km h-1 in 5 s then find
distance travelled by it?
Sol:
u = 0, v = 144 km h-1 = 40 m s-1, t = 5 s
a = (v - u) / t = 8 m s-2
s = 1/2 × 8 × (5)² = 100 m
Example-9:
The driver of a car moving with a velocity of 54 km h-1 applies brakes to decrease its
velocity to 36 km h-1. If the retardation produced by the brakes is 2 m s-2, arrange the
following steps in a sequential order to calculate the distance travelled by the car.
Sol:
u = 54 km h-1 = 15 m s-1, v = 36 km h-1 = 10 m s-1, a = -2.0 m s-1
Using v² - u² = 2as => s = (v² - u²) / (2a)
=> s = (100 - 225) / -2a
=> s = 125 / 4 = 31.25 m
Example-10:
A bike starting from rest picks up a velocity of 72 km h-1 over a distance of 40m. Calculate
its acceleration.
Sol: Given, u = 0, v = 72 km h-1 = 20 m s-1, s = 40m
using v² - u² = 2as => (20)² - 0 = 2a x 40 => a = 400 / 80 = 5 m s-2
Example-11:
A car moving along a straight road with a speed of 72 km h-1 is brought to rest within 3 s
after the application of brakes. Calculate the deceleration produced by the brakes.
Sol:
Initial velocity ‘u’ = 72 km h-1 = 20 m s-1
Final velocity, v = 0 m s-1,
(v - u) / t = a => deceleration = 20 / 3 = 6.67 m s-2
Choose the correct answer:
1. A train starting initially with a speed of 36 km/h picks up a velocity of 108 km/h in
half minute. Calculate its acceleration in m/s².
A) 0.66 m/s² B) 0.76 m/s² C) 0.86 m/s² D) 0.96 m/s²
2. A motor cyclist has 8sec to stop his motor cycle which is travelling at 50 km/h. What is
his retardation?
A) 1.4 m/s² B) 1.74 m/s² C) 1.04 m/s² D) 2.74 m/s²
3. A scooter acquires a velocity of 36 km/h in 10seconds just after the start. Calculate
the acceleration of the scooter.
A) 7m/s² B) 4m/s² C) 3m/s² D) 1m/s²
4. A bus increases its speed from 36km/h to 72km/h in 10seconds. Calculate its
acceleration.
A) 7m/s² B) 4m/s² C) 3m/s² D) 1m/s²
5. If a Ferrari with an initial velocity of 10 m/s accelerates at a rate of 50 ms-2 for 3 s, what will
be its final velocity?
A) 150m/s B) 100 m/s C) 120 m/s D) 160 m/s
6. Josh rolled a bowling ball down a lane in 2.5 s. The ball traveled at a constant acceleration
of 1.8 m/s² down the lane and was traveling at a speed of 7.6 m/s by the time it reached
the pins at the end of the lane. How fast was the ball going when it left Tim’s hand?
A) 1.2 m/s B) 3 m/s C) 3.1 m/s D) 4.1 m/s
7. An aeroplane accelerates down on a runway at 3.20 m/s² for 32.8 s until is finally lifts off
the ground. Determine the distance traveled before takeoff.
A) 1720m B) 1270m C) 1050m D) 1500m
8. A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.
A) 6.4m/s² B) 7.1m/s² C) 8.1 m/s² D) 7.4m/s²
9. A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine
the acceleration of the car and the distance traveled.
A) 73.8m B) 79.8m C) 98.7m D) 89.7m
10. Rocket-powered sleds are used to test the human response to acceleration. If a rocket-
powered sled is accelerated to a speed of 444 m/s in 1.83 seconds then what is the
acceleration and distance that the sled travel?
A) 406m B) 306m C) 206m D) 604m
Multiple option type:
11. A body starting from rest and moving with uniform acceleration of 5 m/s². Then choose
the correct
a) its initial velocity is zero
b) its velocity will increase with time
c) its velocity at the end of 5 sec is 25 m/s
d) its velocity at the end of 10 sec is 250 m/s
A) only a, b, c B) only b, c, d C) only a, c, d D) all a, b, c, d
12. A person running at 20 m/s speeds up to 60 m/s in 4 seconds. Then choose the correct
a) his initial velocity is 20 m/s b) his final velocity is 60 m/s
c) his acceleration is 10 m/s² d) his velocity will be 120 km/h in next 6 sec
A) only a, b, c B) only b, c, d C) only a, c, d D) all a, b, c, d
Fill in the blanks:
13. The velocity of the body decreasing gradually is said to be in...................
14. The S.I unit of deceleration is ....................
15. Another name for deceleration is.....................
Match the following:
16. Column A
a) u = 10m/s, v = 0m/s, t =1s
b) u = 5m/s, v = 5m/s, t =5s
c) u = 0m/s, v = 10m/s, t=5s
d) u = 2m/s, v = 1m/s, t=2s
Column B
1) a = 2m/s²
2) a = -10m/s²
3) a = -0.5m/s²
4) a = 0m/s²
Comprehension type:
17. Acceleration is ratio between change in velocity and time
i) The velocity of car changes from 18 km/h to 72 km/h in 30 s the acceleration in km/h² is
A) 648 B) 6480 C) 64800 D) 648000
ii) The change in velocity of motor bike is 54 km/h in one minute the acceleration in km/h² is
A) 324 B) 3240 C) 32400 D) 324000
iii) A speeding car changes its velocity from 108 km/h to 36 km/h in 4s the deceleration in m/s².
A) 6 B) 5 C) 4 D) 3
Solve the following:
18. A bullet is moving at a speed of 367 m/s when it embeds into a lump of moist clay. The
bullet penetrates for a distance of 0.0621 m. Determine the acceleration of the bullet
while moving into the clay. (Assume a uniform acceleration.)
19. A stone is dropped into a deep well and is heard to hit the water 3.41 s after being dropped.
Determine the depth of the well.
20. A plane has a takeoff speed of 88.3 m/s and requires 1365 m to reach that speed. Determine
the acceleration of the plane and the time required to reach this speed.
Higher order thinking skills (HOTS):
21. A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m.
Determine the acceleration of the bike.
A) 0.8m/s² B) 7.1m/s² C) 0.712 m/s² D) 7.4m/s²
22. An engineer is designing the runway for an airport. Of the planes that will use the airport,
the lowest acceleration rate is likely to be 3 m/s². The takeoff speed for this plane will be
65 m/s. Assuming this minimum acceleration and what is the minimum allowed length
for the runway?
A) 738m B) 798m C) 987m D) 704m
Researchers:
1. What statement best describes the given figure? [NSO-2011]
A) The earth is rotating around the sun B) The sun is rotating around the Earth
C) The Earth is revolving around the sun D) The sun is revolving around the Earth
2. In circular motion the, .......... [NSO-2014]
A) direction of motion is fixed B) direction of motion changes continuously
C) velocity constant D) none
3. Consider the motion of the tip of the minute hand of clock. In one hour. [NSO-2014]
A) The distance covered zero B) the displacement is zero
C) the average speed is zero D) none
4. Which of the following is example of vibratory motion? [NSO-2009]
A) a car moving along a circular track B) a freely falling stone
C) motion of the string of violin D) motion of the planet around the sun
5. Which of the following is example of periodic motion? [NSO-2008]
A) A car taking a turn on a curved road B) A crane filing over a water pond
C) A lift moving down D) march past of soldiers
6. A passenger in a moving train is at ....... w.r.t ground and is at ....... with other passenger in
same train. [NSO-2009]
A) Motion,motion B) rest,rest C) motion, rest D) rest, motion
7. If a body travels half the distance with velocity v1 and the next half with velocity v2,
average velocity will be given by. [NSO-2008]
Vavg = (2v1v2) / (v1 + v2)
8. An artificial satellite is moving in circular orbit of 4225.km. find its speed if it takes 24hr to
revolve around the earth. [NSO-2012]
A) 30.7km/s B) 5.67km/s C) 6.14km/s D) 1.57km/s
9. The length of a square field is 6 m. Parul ran 6 rounds around the field. The total distance that she covered, is ........ [NSO-2008]
A) 216 m B) 144 m C) 176 m D) 186 m
10. Two simple pendulums P and Q are given. P completes 20 oscillations in 32 sec and Q
completes 30 oscillations in 45 sec. Which pendulum is faster? [NSO-2008]
A) P B) Q C) both have same time period D) data insufficiently
11. Two boys P and Q are running along the same path. P is 10 m ahead of Q initially. However,
Q catches up with P. after running 50 m. Assuming that both boys are running at a constant speed. What is the ratio of the speeds of P and Q? [NSO-2014]
A) 6 : 5 B) 5 : 6 C) 4 : 1 D) 4 : 5
12. Sonic vibrations were sent down from a return after 2 seconds. What is the depth of the sea.
If the speed of sound in water is 1.5 kms-1 ? [NSO-2012]
A) 150 m B) 3 m C) 1.5 m D) 750 m
13. A car driver took a total of two hours to make a journey of 75 km. He had a coffee break
of half an hour and spend a quarter of an hour stationary in a traffic jam. What was his
average speed during the journey? [NSO-2012]
A) 38 kms-1 B) 50 kms-1 C) 60 kms-1 D) 75 kms-1
14. Talking one light year equal to 9.4 X 10^15 m and one day equal to 86400 s, what will be the
speed of light in light year per day if the speed of light in ms-1 is 3 X 10^8 ? [NSO-2012]
A) 2.75 X 10-3 ly day-1 B) 3.75 X 10-3 ly day-1
C) 2.75 X 10^3 ly day-1 D) 3.75 X 10-3 ly day-1
15. The ultrasonic waves take 4 second to travel from the ship to the bottom of the sea and
back to the ship (in the form of an echo). What is the depth of the sea? [NSO-2009]
A) 3000 m B) 2000 m C) 1000 m D) 500 m
16. A taxi driver noted reading on the odometer fitted in vehicle as 1050 km, when he started
the journey. After 30 minutes drive, he noted that the odometer reading was 1086 km.
What is the average speed of the taxi? [NSO-2009]
A) 20 m/s B) 25 m/s C) 30 m/s D) 40
17. How long does it take for the earth to rotate on its axis seven times? [NSO-2010]
A) One day B) One week C) One month D) One year
KEY
Teaching Task:
1) A 2) B 3) D 4) C 5) B 6) A 7) D 8) D 9) 5/18
10) instantaneous speed 11) 54 12) 100 13) 50/3 14) D
15) i) A ii) B iii) C 16) 0.444sec 17) 210km 18) 3hr 19) A 20) A
21) A 22) B
LEARNER’S TASK
BEGINNERS (Level - I)
1) A 2) D 3) A 4) B 5) D 6) B 7) D 8) C 9) B 10) A 11) D
12) C 13) A 14) D 15) zero 16) 5 m 17) displacement, distance 18) A
19) a) 440 m, 0 m b) 880 m, 0 m c) 220 m, 140 m d) 110 m, 140 m e) 330 m,
140 m 20) 11.6 m 21) 9 km, 6.7 km 22) 8.94 m 23) 5 km
24) SE 25) 2R 26) 30 cm, 0 cm 27) 2:π
RESEARCHERS:
1) C 2) B 3) B 4) C 5) D 6) C 7) Vavg = (2v1v2)/(v1+v2),
8) A 9) B 10) B 11) D 12) C 13) C 14) A 15) A 16) A
17) B