Motion

IMPORTANT NOTES
1. Rest : When a body does not change its position 13. Average speed : The average distance covered by
with respect to time and its surroundings, the a body per unit time, when the body is moving
body is said to be at rest. with a variable speed is called average speed.
2. Motion : When a body continuously changes 14. Velocity : The distance covered by a body
its position with respect to time and its per unit time in a specified direction is called
surroundings, the body is said to be in velocity. It is vector quantity and has same
motion. units as speed.
3. Locomotion : The motion performed by 15. Uniform velocity : When a body covers equal
living beings (animals and plants) is called distances in equal intervals of time (however
locomotion. small may be the time intervals) in a specified
4. Characteristics (properties) of a moving direction, the body is said to be moving with
body : uniform velocity.
(i) There must be a reference point (a stationary 16. Variable velocity or Non-uniform velocity :
When a body covers unequal distances in equal
object) to describe the position of a given
intervals of time in a specified direction or
body. when a body covers equal distances in equal
(ii) The position of the given body must
L S
intervals of time, but its direction changes, then
the body is said to be moving with a variable
continuously change with time and with
respect to reference point.
R velocity.IA
5. Distance : It is the actual length of the path
travelled by a moving body, irrespective of the T O 17. Acceleration : The rate of change of velocity
of a moving body is called acceleration. It is
direction of motion of the body.
T U vector quantity and its unit is metre per square
second (ms–2 or m/s2).

N I L
6. Displacement : The shortest distance of a
moving body from the point of reference (initial 18. Positive acceleration : The rate of change of
A
position of the body) in a specified direction
is called displacement.
velocity of a moving body, when the velocity
is increasing is called positive acceleration.
7. Uniform motion : When a body covers equal 19. Negative acceleration : The rate of change of
distances in equal intervals of time, however velocity of a moving body, when the velocity
small may be time intervals, the body is said is decreasing is called negative acceleration or
to describe uniform motion. retardation.
8. Non-uniform motion : When a body covers 20. Conclusions from a distance-time graph.
unequal distances in equal intervals of time, it is (i) If the graph is parallel to the time axis,
said to be moving with non-uniform motion. then the body is stationary.
9. Speed : The rate of change of motion is called (ii) If the graph is a straight line, but not parallel
the speed. to time axis then the body is moving with
10. Mathematical expression for speed : Speed a uniform speed.
= Distance ÷ Time. SI unit of speed is metre (iii) If the graph is a curve, it implies that body
per second (ms–1 or m/s). is moving with a variable speed and has
11. Uniform speed : When a body covers equal accelerated motion.
distances in equal intervals of time, however 21. Conclusions from a velocity-time graph.
small may be the time intervals, the body is (a) When the velocity-time graph is a straight
said to be moving with uniform speed. line parallel to time axis.
12. Variable speed : When a body covers unequal
(i) The body is moving with a uniform
distances in equal intervals of time, the body
velocity and its acceleration is zero.
is said to be moving with variable speed.

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 (ii) The displacement of body can be calculated (iii) The displacement of a body can be
from the area under graph line. calculated by finding area under the
(b) When the velocity-time graph is a straight velocity-time graph line.
line, but not parallel to time axis. 22. If a body having initial velocity ‘u’ is acted
(i) The body is moving with a variable upon an acceleration ‘a’ for the time ‘t’ such
that ‘v’ is its final velocity and s is distance
velocity, but uniform acceleration.
covered then :
(ii) The uniform acceleration/deceleration 1
can be calculated by finding slope of (i) v = u + at (ii) s = ut + at2
2
the graph. If the slope is positive then (iii) v2 = u2 + 2as
it is positive acceleration. If slope is 23. Uniform circular motion : When a body moves
negative then it is retardation. in a circular path with uniform motion.

Assignments for summAtive Assessment

I. VeRy ShoRt ANSWeR QUeStIoNS (1 MARk)
PReVIoUS yeARS' QUeStIoNS
1. State the meaning of uniform circular motion. What is its displacement when it completes 11/2
[2010 ( -I)] revolutions. [2010 ( -I)]
2. Why is the motion of an athlete moving along 7. What kind of motion of a body is represented
the circular path an accelerated motion ? by the graphs given below? [2010 ( -I)]
[2010 ( -I)]
L S
3. State the type of motion represented by the given
graph. [2010 ( -I)]
R IA
D T O
i
s T U
t
a
N I L
n
c
A 8. "The direction in which an object moves is given
e by the direction of velocity of the object and
Time not by the direction of acceleration". Give an
4. If the acceleration of the particle is constant in example to justify this statement. [2010 ( -I)]
magnitude but not in direction, what type of 9. Velocity-time graph for a moving body is shown
path does the particle follow ? [2010 ( -I)] in the diagram. What conclusion can be drawn
5. Two cars A and B have their displacement-time about the type of motion? [2010 ( -I)]
graph as given below. Which car has a greater
velocity? [2010 ( -I)]

10. Velocity of a particle moving along a straight line

in a certain time interval is shown below. What
is the distance travelled during acceleration?
6. A particle is moving in a circle of diameter 5 m. [2010 ( -I)]

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 13. An object starts with initial velocity u and attains
a final velocity of v. The velocity of the object
is changing at a uniform rate. [2010 ( -I)]
Write the formula for calculating the average
velocity vav.
14. A body thrown in the vertically upward direction
rises up to a height 'h' and comes back to the
position of start. Calculate.
11. Name the quantity measured by the area occupied
below the velocity - time graph. [2010 ( -I)] (a) the total distance travelled by the body
12. Under what condition is the magnitude of distance (b) the displacement of the body. [2010 ( -I)]
and displacement equal? [2010 ( -I)]

otheR IMPoRtANt QUeStIoNS

1. When is a body said to be at rest? 15. Amongst speed and velocity which is a scalar
quantity and why?
2. When is a body said to be in motion?
16. A body is covering 4 m in every 1 second
3. Give an example, when a body is at rest as well for 10 seconds towards east. What physical
as in motion. quantity does the body represent and state its
4. Give the name of a physical quantity that magnitude?
corresponds to the actual path travelled by a 17. A body covers a distance of 5 m in the first
moving body. second, 10 m in the second second and 15 m
5. Give the name of the physical quantity that L S
in the third second, all distances being covered
corresponds to the shortest distance between
the initial and the final position of a moving R IA
towards the west. What physical quantity does
the body represent?
body.
T O 18. The velocity of a body increases by 10 m/s in
TU
6. Which amongst the following is a vector quantity
L
every one second. What physical quantity does
the body represent and what is its magnitude?

N I
and why? (i) Distance (ii) Displacement.
19. A train running at 20 ms–1 slows down at a rate
terms? A
7. Are rest and motion relative terms or opposite
of 1 ms–1 in every one second, till the train stops.
Is the train acted upon by negative or positive
8. What kind of bodies show locomotion in nature? acceleration and state its magnitude?
9. Give the name of the physical quantity that 20. A cricket ball is projected vertically upwards.
corresponds to the rate of change of motion and What kind of acceleration is acting on the
state its unit in SI system. ball?
10. Does the motion of seconds hand of a watch 21. The distance-time graph of a body is a straight
represent uniform velocity or uniform speed? line parallel to the time axis. What information
does the graph convey regarding the motion of
11. Does the seconds hand of a watch represent
the body?
uniform motion or accelerated motion?
22. Which physical quantity can be calculated by
12. A boy runs around a circular park of radius 7 m
finding the slope of a distance-time graph?
in 11 seconds. What is the speed of the boy?
23. Area under the velocity-time graph line is
13. Give the name of a physical quantity that
40 m. What physical quantity does this area
corresponds to the rate of change of motion in
represent?
a specified direction.
24. How can you calculate acceleration from a
14. What do you understand by the term non-uniform
velocity-time graph?
motion? Give an example.

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 II. ShoRt ANSWeR QUeStIoNS – I (2 Marks)
PReVIoUS yeARS’ QUeStIoNS

1. A cyclist travels a distance of 4 km from P to 10. What do the graphs shown below indicate :
Q and then moves a distance of 3 km at right [2010 ( -I)]
angle to PQ. Find his resultant displacement
graphically. [2010 ( -I)]
2. A bus decreases its speed from 80 km/h to 50
km/h in 4 s. Find the acceleration of the bus.
[2010 ( -I)]
3. An electric train is moving with a velocity of
120 km/hr. How much distance will it cover in
30 s? [2010 ( -I)]
4. Giving one example each distinguish between 11. On a 120 km track, a train travels the first
uniform acceleration and non-uniform 30 km at a uniform speed of 30 km/h. Calculate
acceleration. [2010 ( -I)] the speed with which the train should move rest
5. Represent the given data graphically. of the track so as to get the average speed of
[2010 ( -I)] 60 km/h for the entire trip? [2010 ( -I)]
12. The following displacement - time graph shows
TIME (IN SEC) DISTANCE (M) the positions of a body at different times.
Calculate the velocity of the body as it moves
0 0 from
L S [2010 ( -I)]

2 5
R IA
T O
4 10
T U
6
N I 20 L
graphs.
A
6. Explain the differences between the two
[2010 ( -I)]

(i) A - B
(ii) B - C
(iii) C - D
13. An athlete completes one round of a circular
track of diameter 49 m in 20 s. Calculate the
distance covered and displacement at the end of
30 s. [2010 ( -I)]
7. A particle moves 3 m north, then 4 m east and 14. The graph given below is the distance - time
finally 6 m south. Calculate the displacement. graph of an object. [2010 ( -I)]
[2010 ( -I)]
(i) Find the speed of the object during first four
8. A body can have zero average velocity but not seconds of its journey
zero average speed. Justify. [2010 ( -I)]
(ii) How long was it stationary?
9. A train 100 m long is moving with a velocity
(iii) Does it represents a real situation? Justify
of 60 kmh–1. Find the time it takes to cross the
your answer.
bridge 1 km long. [2010 ( -I)]

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 whether the motion of the objects is uniform or
non uniform. Give reasons. [2010 ( -I)]

ime Distance Distance

travelled by travelled by
object A in m. object B in m.
9.30 a.m 10 12
9.45 a.m 20 19
10.00 a.m 30 23
10.15 a.m 40 35
15. A car covers a distance x, while moving at 54 10.30 a.m 50 37
km/hr in 15 sec. The value of x is 10.45 a.m 60 41
(a) 2.25 km 11.00 a.m 70 44
(b) 5.40 km
20. A girl moves with the speed of 6 km/h for 2 h
(c) 0.225 km
and with the speed of 4 km/h for the next 3 h.
(d) 13.5 km Find the average speed of the girl and the total
Choose the correct answer workout to arrive at distance moved. [2010 ( -I)]
the answer. [2010 ( -I)] 21. Four speed - time graphs are shown below.
16. A marble rolling on a smooth floor has an [2010 ( -I)]
initial velocity of 0.4 m/s. If the floor offers a
retardation of 0.02 m/s2, calculate the time it
will take to come to rest. [2010 ( -I)]
17. (a) What does the odometer of an automobile
L S
measure? [2010 ( -I)]
(b) Two graphs for motion of objects moving along R IA
a straight line are shown. State how the speed
T O
is changing with time in both the cases.
T U
N I L
A
18. A person travelling in a bus noted the timings
and the corresponding distances as indicated on
the km stones. Which graph represents the following case?
ime Distance (a) A ball thrown vertically upwards and returning
8.00 am 10 km to the hand of the thrower?
8.15 am 20 km (b) A body decelerating to a constant speed and
8.30 am 30 km then accelerating.
8.45 am 40 km Speed (m/s) Time (s)
9.00 am 50 km (a) (b)
(a) Name this type of table. (c) (d)
(b) What conclusion do you draw from this 22. A farmer moves along the boundary of a square
data? [2010 ( -I)] field of side 10 m in 40 s. What will be the
19. Examine the data given below for motion of magnitude of displacement of the farmer at the
two different objects A and B carefully and state end of 2 min. 20 s? [2010 ( -I)]

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 23. The minute hand of a wall clock is 10 cm long. at rate 5 m/s2. Find the final velocity when the
Find its displacement and the distance covered car has travelled a distance 30 m. [2010 ( -I)]
from 10 a.m to 10.30 a.m. [2010 ( -I)] 25. A body covers a semicircle of radius 7 cm in 5
24. A car starts with velocity 10 m/s and accelerates second. Find its velocity. [2010 ( -I)]

otheR IMPoRtANt QUeStIoNS

1. State two differences between scalar and vector 9. Define the terms :
quantities. (i) speed and (ii) velocity.
2. State two differences between distance and 10. Why is speed considered an incomplete physical
displacement. quantity? Name a quantity akin to speed
3. State two differences between speed and which describes the motion of a particle more
velocity. accurately.
4. A car moving along a circular path of radius 11. Name a physical quantity which corresponds
140 m, completes one round in 20 s. What is to:
(i) the speed of the car (ii) the displacement (a) rate of change of displacement
of the car?
(b) rate of change of velocity
5. Give an example of a body moving with a
uniform speed and uniform acceleration. Justify 12. Arrange the following speeds in the increasing
your answer. order :
6. (a) What do you understand by the term : (i) A scooter moving with a speed of 300 m
(i) Distance (ii) Displacement? (b) State the SI per minute.
units of distance and displacement. (ii) A car moving with a speed of 27 km per
7. A body is moving along a circular path of
radius R. What will be the distance covered
hour.
L S
13. Draw a diagram to show the motion of a body
and the displacement of the body after half
revolution? R IA
whose speed remains constant, but the velocity
changes continuously.
8. A person starts from his house and travels a
T O 14. Draw a velocity versus time graph of a stone

T U
circular distance of 15 km around the walled city
before returning back. What is (a) the distance
thrown vertically upwards and then coming
downwards after attaining the maximum

the person? N I L
covered by the person, (b) the displacement of height.

A
III. ShoRt ANSWeR QUeStIoNS – II (3 Marks)
PReVIoUS yeARS’ QUeStIoNS
1. What can you conclude about the motion of 2. Derive the equation v2 – u2 = 2as graphically.
a body depicted by the velocity-time graphs [2010 ( -I)]
(i), (ii) and (iii) given below : [2010 ( -I)]
3. A bus travels at a distance of 120 km with a
speed of 40 km/h and returns with a speed of
30 km/h. Calculate the average speed for the
entire journey. [2010 ( -I)]
4. A bus accelerates uniformly from 54 km/h to
72 km/h in 10 s. Calculate : [2010 ( -I)]
(i) the acceleration
(ii) the distance covered by the bus in that
time
5. (a) An object travels 16 m in 4 seconds and
the next 16 m in 2 seconds. Calculate the
average speed of the object.
(b) Give an example of an object moving under
uniform circular motion. [2010 ( -I)]

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 6. The driver of a train A travelling at a speed of 11. Joseph jogs from one end A to the other end B
54 km/h applies brakes and retards the train of a straight 300 m road in 2 minutes 50 seconds
uniformly. The train stops in 5 s. Another train and then turns around and jogs 100 m back of
B is travelling on the parallel track with a speed point C in another 1 minute. What are Joseph's
of 36 km/h. This driver also applies the brakes average speeds and velocities in jogging?
and the train retards uniformly. The train B (a) from A to B and (b) from A to C?
stops in 10 s. Plot speed - time graph for both [2010 ( -I)]
the trains on the same paper. Also calculate the
distance travelled by each train after the brakes 12. Rajeev went from Delhi to Chandigarh on his
were applied. [2010 ( -I)] motorbike. The odometer of the bike read 4200 km
at the start of trip and 4460 km at the end of his
7. (a) A car accelerates uniformly from 18 kmh–1 to trip. If Rajeev took 4 h 20 minutes to complete
36 kmh–1 in 5 s. Calculate : his trip, find the average speed in kmh–1 as well
(i) acceleration as ms–1. [2010 ( -I)]
13. Draw a graph velocity versus time for a body
(ii) distance covered by the car in that
starts to move with velocity 'u' under a constant
time. [2010 ( -I)] acceleration a for time t. Using this graph derive
(b) The length of minute hand of a clock is 14 cm. an expression for distance covered 's' in time 't'.
Calculate the speed with which the tip of the [2010 ( -I)]
minute hand moves. 14. Ali while driving to school, computes the average
8. A car is moving on a straight road with a uniform speed for his trip to be 20 km/h. On his return
acceleration. The following table gives the speed trip along the same route there is less traffic
of the car at various instants of time. and the average speed is 30 km/ h. What is the
average speed for Ali's trip? [2010 ( -I)]
[2010 ( -I)]
15. The brakes applied to a car produce an
Time (s)
Speed (ms )–1
0
5
10
10
20
15
30
20
40
25
50
30 L S
acceleration of 6 m/s2 in the opposite direction
to the motion. If the car takes two seconds to
(i) Draw the shape of speed - time graph
R IA
stop after the application of brakes, calculate
the distance it travels during this time.
representing the above sets of observations.
T O [2010 ( -I)]

9.
(ii) Find the acceleration of the car.
T U
[2010 ( -I)]
16. While driving Jayant travels 30 km with a speed
of 40 km/h and next 30 km with a uniform speed

N I L of 20 km/h. Find his average speed.

[2010 ( -I)]
A 17. A train accelerates uniformly from 36 km/hr to
54 km/hr in 10 seconds. Find
(a) the acceleration
(b) the distance travelled by the car during this
interval of time. [2010 ( -I)]
18. A van is accelerated uniformly from 36 km
per hour to 90 km per hour in 3 seconds.
Calculate: [2010 ( -I)]
(i) the acceleration
(ii) the distance covered by the van in that
time
19. Thread
From the given data find the value of 'a' (i) from
A to B (ii) from B to C (iii) from C to D
10. Starting from a stationary position , Rehan
paddles his bicycle to attain a velocity of 6 m/s
in 30 s. Then he applies brakes such that the Stone
velocity of the bicycle comes down to 4 m/s in
the next 5 s. Calculate the acceleration of the
bicycle in both the cases. [2010 ( -I)]

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 Look at the figure above : Look at the figure above :
(a) Name the kind of motion of the stone. An object starts its journey from point 0. A,
(b) Is this an example of accelerated motion? B, C, D and E represent position of the object
Why? at different instants. The object moves through
A, B, C, D and E and then moves back to
(c) Name the force that keeps the stone in its point C.
path.
Calculate :
(d) What is the direction of this force? Draw it
in your answer sheet. [2010 ( -I)] (a) the distance travelled by the object
20. (b) the displacement of the object
(c) name the reference point in the diagram

[2010 ( -I)]

otheR IMPoRtANt QUeStIoNS

1. By giving one example each, define : (a) uniform initial position. Her displacement-time graph is
velocity. (b) variable velocity and (c) average shown in the figure. Plot a velocity-time graph for
velocity. the same.
2. Suggest what kind of motion of a body is
represented by the graph given below :

Displacement (m)
100
S
Distance

Distance

IA L
O R
Time Time
U T 0 50
Time (s)
100

L T 7. A car starts from rest and moves along the

NI x-axis with a constant acceleration of 5 m s–2

Distance

A for 8 seconds. If it then continues to move with

a constant velocity, what distance will the car
cover in 12 seconds since it started from rest?
Time 8. A motorcyclist drives from A to B with a uniform
speed of 30 km h–1 and returns back with a speed
3. Draw the distance-time graph for the following of 20 km h–1. Find its average speed.
situations :
9. The velocity-time graph shows the motion of a
(a) When a body is stationary. cyclist. Find (i) its acceleration (ii) its velocity
(b) When a body is moving with a uniform and (iii) the distance covered by the cyclist in
speed. 15 seconds.
(c) When a body is moving with variable speed
and uniform acceleration.
4. The displacement of a moving object in a given
interval of time is zero. Would the distance
travelled by the object also be zero? Justify your
answer.
5. How will the equations of motion for an object
moving with a uniform velocity change?
6. A girl walks along a straight path to drop a
letter in the letter box and comes back to her
8

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 10. A car is running at a speed of 54 km h–1. In the velocity and uniform acceleration.
next second, its speed is 63 km h–1. Calculate (c) When the body is moving with variable
the distance covered by the car in m. velocity and uniform deceleration.
11. Draw velocity-time graphs for the following 12. How can you calculate the following :
situations :
(a) Speed from distance-time graph.
(a) When the body is moving with uniform
velocity. (b) Acceleration from velocity-time graph.

(b) When the body is moving with variable (c) Displacement from velocity-time graph.

IV. LoNg ANSWeR QUeStIoNS (5 Marks)

PReVIoUS yeARS’ QUeStIoNS

1.

L S
R IA
T O 3. (a) Prove that v = u + at, using graphical

L TU method [2010 ( -I)]

N I (b) A train starting from rest attains a velocity

of 72 km/h in 5 minutes. Assuming the
A
The V-T graph of cars A and B which start from
the same place and move along a straight road
acceleration is uniform. Find

in the same direction, is shown. Calculate (i) the (i) the acceleration
acceleration of car A between 0 and 8 s. (ii) the (ii) the distance travelled by the train for
acceleration of car B between 2 s and 4 s. (iii) attaining this velocity.
the points of time at which both the cars have the
same velocity (iv) which of the two cars is ahead 4. The distance - time graph of two trains are
after 8 sec. and by how much? [2010 ( -I)] given below. The trains start simultaneously in
the same direction. [2010 ( -I)]
2. (a) The velocity-time graph of a car is given below.
The car weighs 1000 kg. [2010 ( -I)] (i) How much ahead of A is B when the motion
starts?
(i) What is the distance travelled by the car in
the first 2 seconds? (ii) What is the speed of B?
(ii) What is the braking force at the end of 5 (iii) When and where will A catch B?
seconds to bring the car to a stop within one
(iv) What is the difference between the speeds
second?
1 of A and B?
(b) Derive the equation S = ut + at2 using
graphical method.
2 (v) Is the speed of both the trains uniform or
non-uniform? Justify your answer.

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 otheR IMPoRtANt QUeStIoNS

1. Suggest real life examples where the motion Use this graph to find average velocity for the
of a body is similar to that represented by the first 4 s, for the next 4 s and for the last 6 s.
following velocity-time graphs : 5. An electron moving with a velocity of 5 × 104
ms–1 enters into a uniform electric field and
acquires a uniform acceleration of 104 ms–2 in
the direction of its initial motion.
(i) Calculate the time in which the electron
would acquire a velocity double of its initial
velocity.
(ii) What distance would the electron cover in
this time?
6. Two stones are thrown vertically upwards
simultaneously with their initial velocities u1 and
u2 respectively. Prove that the heights reached by
2. An object is dropped from rest at a height of 2 2
them would be in the ratio of u1 : u 2 (Assume
150 m and simultaneously another object is upward acceleration to be –g and downward
dropped from rest at a height 100 m. What is acceleration to be +g).
the difference in their heights after 2 s if both 7. A train starting from rest, picks up a speed of
the objects drop with same acceleration? How 20 ms–1 in 200 s. It continues to move at the
does the difference in heights vary with time? same speed for the next 500 s. It is then brought
3. An object starting from rest travels 20 m in the
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to rest in the next 100 s.
first 2 s and 160 m in the next 4 s. What will
be the velocity after 7 s from the start?
R
(i)
(ii) IA
Plot a speed time graph.
Calculate the rate of uniform acceleration.
4. Using the following data, draw time-displacement
T O (iii)Calculate the rate of uniform retardation.
graph for a moving object :
T U (iv) Calculate the distance covered by the train
during retardation.
ime (s)
Displacement (m)
0 2
0 2
4
4
6
4
N
8
I
4 6 L
10 12 14 16
4 2 0 (v) Calculate the average speed during
retardation.
A

B
D

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