QUESTIONS RELATED TO LINEAR MOTION

1. (a) Define the terms distance, displacement, and velocity.

(b) An object moving at a constant speed of 200 m in 8 s. Find the object speed. (Ans: 25 m s-1)
(c) An object traveling at a constant speed travels 3 km in 2 min. Find the speed of the object.
(Ans: 25 ms-1)

2. At t = 0 s, an object passes point A at a constant speed of 4 m s-1.

(a). Find the distance from point A to the object at t = 3 s.
(b). Find the time spent after traveling 22 m from point A. (Ans: (a). 12 m (b). 5.5 s)

3. Convert units to the following speeds as required.

(a). Convert speed of 36 km h-1 into m s-1.
(b). Convert speed of 81 km h-1 into m s-1.
(c). Convert speed of 35 m s-1 in km h-1
(d). Convert speed 22 m s-1 speed in km h-1.
(e). Present speed of 6 km min-1 in m s-1.
(Ans: (a). 10 m s-1 (b). 22.5 m s-1 (c). 126 km h-1 (d). 79.2 km h-1 (e). 100 m s-1)

4. (a). Define the velocity.

(b). What do average speed and average velocity mean?
(c). A, B and C are three points on a straight line, AB = 5 km, and BC = 4 km, respectively. Man
runs from A to B at a speed of 20 km h-1, and from B to C at a speed of 8 km h-1.
(i). Find the total time taken to go from A to C.
(ii). Find the average speed of the journey from A to C (Ans: (i) 45 min, (ii). 12 km h-1)

5. A man walks 150 m to the north in 70 s and then 50 m to the south in 30 s.

(a). Find his average speed.
(b). Find his average velocity.
(Ans: (i) 2 m s-1, (ii) .1 m s-1 to the north)

6. A train travels 50% of its journey at a speed of 10 m s-1 and the rest of the journey is travelled at
speed of 15 m s-1. What is the average speed of the train during the entire journey?
(Ans: 12 ms-1)

7. A child runs at a speed of 45 m s-1 on the straight road from his home to school and returns to his
home at a speed of 2 m s-1.

(a). What is the average of his speed? (Ans: 2.67 m s-1)

(b). What is the average of the velocity? (Ans: 0 m s-1)

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8. A is a ball smaller than B, located 20 m farther away from B ball, travels in a straight path at a
speed of 5 m s-1 toward the B ball. After hitting with B ball, the A ball returns to its initial position
along the path it went at a speed of 4 m s-1.
(a). Calculate the average velocity of A. (Ans: 5 m s-1)
(b). Calculate the average velocity in the time periods of 0-4 s/ 0 s – 6 s/ 0 s – 9 s
(Ans: 5ms-1 / 4.44 m s-1/ 4.67 m s-1)

9.
(a). Define speed and velocity.
(b). Explain the difference between speed and velocity.
(c). What is the average velocity of a moving object?
(d). During the movement of a car, 1/3 of the time is spent at V1 speed, the other 1/3 of the time
at V2 speed and the remaining 1/3 of the time at V3 speed. Show that the average speed of the
𝑉1 +𝑉2 +𝑉3
vehicle is .
3

10. When one vehicle is in motion, 1/3 of the total displacement is at V1 speed, the other 1/3
displacement is at V2 speed, and the remaining 1/3 displacement is at V3 speed. Show that the
3𝑉1 𝑉2 𝑉3
average speed of the vehicle is .
𝑉1 𝑉2 +𝑉2 𝑉3 +𝑉3 𝑉1

11. Find the average speed and average velocity of each journey below.

a) When a train travels at a speed of 10 m s-1 for one minute, another 2 minutes at a speed of
15 m s-1, and the last 3 minutes at a speed of 12 m s-1.
b) When going from X to Y at a speed of 5 ms-1 and coming back from Y to X at a speed of
10 ms-1
c) Starting at rest, it travels for 5 seconds at a uniform acceleration of 1 m s-2
d) Starting at rest, it travels for 20 seconds at a uniform acceleration of 0.5 m s-2 and travels
with that obtained velocity with the same direction for one minute.
(Ans. (i). 12.67 m s-1, 12.67 m s-1 (ii). 6.67 m s-1, 0 (iii). 2.5 m s-1, 2.5 m s-1 (iv). 8.75 m s-1, 8.75 m s-1)

12. (a). Define the acceleration of an object.

(b). The time taken for a car to travel at a speed of 5 m s-1 and pass a point 30 m away is 4 s.
What is the acceleration of the vehicle and the speed obtained at the end of 4 s?

13. In the following problems, object starts at an initial velocity U and travels with 𝒂 uniform
acceleration and obtained 𝑽 velocity after 𝒕 time.

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 (a). Find 𝑡, if 𝑈 = 0, 𝑎 = 3 𝑚 𝑠−2, 𝑉 = 15 𝑚 𝑠−1

(b). Find 𝑉, if 𝑈 = 6 𝑚 𝑠−1, 𝑆 = 24 𝑚 , 𝑡 = 10 𝑠

(c). Find 𝑉, if 𝑈 = 4 𝑚 𝑠−1, 𝑆 = 2 𝑚 , 𝑎 = 5 𝑚 𝑠−2

(d). Find 𝑆, if 𝑈 = 16 𝑚 𝑠−1, 𝑉 = 8 𝑚 𝑠−1 , 𝑡 = 5 𝑠

(e). Find 𝑎, if 𝑈 = 3 𝑚 𝑠−1, 𝑉 = 17 𝑚 𝑠−1 , 𝑡 = 7 𝑠

14. An object that starts at rest moves first with uniform acceleration, second with a uniform velocity
of 10 m s-1, and the last with a uniform deceleration. If the total time for the journey is 160 s and
the displacement is 1.2 km, find the distance traveled by the object at uniform velocity and if the
acceleration is 0.5 m s-2, find the deceleration. (Ans: 800 m, 1/6 m s-2).

15. Anyone who observes the motion of an object moving at a uniform acceleration will see that the
object travels 500 m within 10 s. In the next 10 s it will move 700 m. If the object started moving
at rest, find the time elapsed when the observer saw it and the displacement that has already taken
place. (Ans: 20 s, 400 m)

16. In a car race, two cars A and B start at rest and move a1 and a2 constant accelerations. When A
reaches the end point, A has a greater velocity than B by the amount of v and time taken by A is
lesser than B by the amount of t. Prove that 𝑣2 = 𝑎1𝑎2𝑡2.

17. A vehicle starts at rest and travels in a straight-line d distance with uniform acceleration and then
travels the next 2d distance with uniform velocity and then travels 3d distance with uniform
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 3
deceleration and comes at rest. Prove that 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 5.

18. A car starts at rest and travels for some time at a uniform acceleration of 5 m s-2, and then at a
uniform speed for another time. The vehicle then moves with a uniform deceleration of 5 m s-2
and comes to a standstill at some point. The total time taken for the trip is 25 s. If the average
speed of the whole journey is 20 m s-1, find the time at which the vehicle traveled at a uniform
velocity. (Ans: 15 s)

19. An object travelling at a uniform acceleration in a straight line travels a distance of x and y at t1
2(𝑦𝑡1 −𝑥𝑡2 )
and t2 intervals, respectively. If the acceleration of the object is a, then prove that (𝑡 .
1 +𝑡2 )𝑡1 𝑡2

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20. An object travelling at uniform acceleration travels equal displacements at t1, t2 and t3 time
1 1 1 3
intervals. Prove that 𝑡 + 𝑡 + 𝑡 = 𝑡 .
1 2 3 1 +𝑡2 +𝑡3

21. A train which was travelling with uniform velocity of 20 m s-1 suddenly began to accelerate with
the magnitude of 2 m s-2 for 20 s time period. What was the displacement achieved by the train
during that time period and find the velocity at the end of the time period?

22. A car was travelled with the uniform velocity of 36 km h-1 and suddenly 1m s-2 deacceleration
was given until the rest by breaking. How long that the car was deaccelerated and find the
displacement travelled under deacceleration.

23. A car was at rest at point A and then it moved to point B under acceleration. From B to C, it
travelled with a uniform velocity of 10 ms-1 and from C to D began to deaccelerate with the
magnitude of 2m s-2. Finally, it was stopped at D. the time taken for the whole journey was 35 s.
if BC is 200 m, then find the acceleration in A to B. find the distance travelled under acceleration,
time taken under acceleration, distance travelled under deacceleration.

24. Particle moves with a constant acceleration from A to B. V1 and V2 are velocities at A and B
respectively. if C is the middle point of the path, then find the velocity at C in terms of V1 and V2

25. The vehicle accelerated for 6 s and reached to 18 m s-1 from rest. It continued that reached velocity
for 12 s and began to deaccelerate. Find acceleration, deacceleration and the displacement.

26. A man suddenly observed that an object is moving with a constant acceleration. It travelled 500
m within 10 s and the very next 10 s, it moved 700 m. If the object started moving from rest, what
is the time and distance taken by the object from rest until man’s very first observation.

27. A car has gone its first half of the journey with the constant velocity of V1 and next half of the
journey with the velocity of V2. Find the average velocity of the whole journey.

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28. A particle moves from A to B with a constant velocity of V and from B to C constant velocity of
2V. Finally with the constant velocity of 3V, it moves from C and reaches to A. Find the average
velocity within the total destination.

29. A motion of a vehicle began from rest, and it moves with a constant acceleration. If the velocity
after n seconds was V, then what was the displacement achieved by the vehicle for last 2 seconds.

30. The length of the second hand of a clock is 5 cm. Find the displacement, average speed and
average velocity of the tip of the second hand in below time intervals.
a. 0 s – 15 s
b. 0 s – 30 s
c. 0 s – 60 s

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 Motion Graphs
Displacement – time graphs (s – t Graphs)

When an object moving in a straight line, a graph drawn between displacement and time by measuring
the displacements corresponding to the time is called as displacement - time graph.

➢ When drawing any graph of vectors, vectors to the one direction should be considered as
positive (+).

Intercept
 The intercept on Y axis in a s – t graph denotes the displacement when t = 0.
 If the displacement is measured from the position of the object at t=0, then intercept is zero.

Coordinates of points
 The x-coordinate represents the time, and the y-coordinates represent the displacement
corresponding to each time.
 Time may not be negative, but the displacement may be positive or negative.

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Page 7 of 27
 Gradient / Slope

In a displacement – time graph, the gradient at a point on the graph denotes the velocity at that point.

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 Information gained from a s – t graph

1. …………………………………………………………………………………………………
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2. …………………………………………………………………………………………………
………………………………….

Velocity – time graph

 A graph drawn by measuring the velocity with time of an object moving in a straight line is
called a velocity-time graph.
 Velocity to the one direction is considered as positive (+) then velocity to the other direction
is considered as negative (-).

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Intercept
 The intercept on Y axis in a v – t graph denotes the velocity when t = 0.
 If the displacement is measured from the position of the object at t=0, then intercept is zero.

Coordinates of points
 The x-coordinate represents the time, and the y-coordinates represent the velocity
corresponding to each time.
 Time may not be negative, but the velocity may be positive or negative.

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Page 11 of 27
Gradient / Slope

In displacement -times graph, the gradient at a point on the graph denotes the velocity at
that point.
–

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 ➢ Since the acceleration of most of the problems we solve is constant, the graph drawn for
v - t takes the shape of a straight line.

Area under the graph

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  (1) = (2) indicates that the area under a graph v - t represents the displacement difference
over time.

 The algebraic area of a given time in a v - t graph, represents the total displacement of
the object at that time.

 In a v - t graph, the sum of the magnitudes of the areas specified over a period of time in
a graph representing the total distance traveled by the object at that time.

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Information gained from v – t graph

1. ………………………………………………………………………………………………………
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2. ………………………………………………………………………………………………………
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3. ………………………………………………………………………………………………………
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When the velocity - time graphs of two objects are represented in the same coordinate plane, the
intersection of the two graphs represents the moment when the velocities of the two objects are equal.

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Acceleration – time graph (a – t graph)

a a

 A graph drawn by measuring the acceleration with time of an object moving in a straight line
is called acceleration - time graph.
 acceleration to one direction is considered as positive (+) then acceleration to the opposite
direction is considered as negative (-).
Intercept
➢ The intercept on Y axis in a – t graph denotes the acceleration when t = 0.

Coordinates of points
 The x-coordinate represents the time and the y-coordinates represent the acceleration
corresponding to each time.
 Time may not be negative but the acceleration may be positive or negative. Gradient /

Slope

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Area under graph

Information gained from a – t graph

1. …………………………………………………………………………………………………
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2. …………………………………………………………………………………………………
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When the acceleration - time graphs of two objects are represented in the same coordinate plane, the
intersection of the two graphs represents the moment when the acceleration of the two objects are
equal.

Conversions of graphs Converting a s- t graph into a v-t graph

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1. ………………………………………………………………………………………………………
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Converting a v – t graph in to s – t graph

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Note

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…………………………………………………………………………………………………………
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Converting a - t graph into a v-t graph

3. …………………………………………………………………………………………………
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4. …………………………………………………………………………………………………
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Converting a v – t graph in to a – t graph

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 3. …………………………………………………………………………………………………
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 QUESTIONS RELATED TO MOTION GRAPH

1. Draw v-t graphs for the below s-t graphs.

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2. Draw s-t graphs for below v-t graphs

v v v v

v v v

v v v v

v v v v

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3. Draw v-t graphs for below a-t graphs

4. Draw 1-t graphs for below v-t graphs

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5. The s-t graph is drawn below for an object which moves to the positive x direction from
origin.

a. Find the initial velocity of the object

b. Find the terminal velocity of the object
c. How long the object was at rest?
d. At which point, thedirection of the motion of the
object is changed.
e. What is the time taken to pass the origin again?
f. Draw the v-t diagram relevant to above -t diagram
s

. (Take𝜃 = 𝑠𝑖𝑛−1 (4/√17))

6. V-t graph is drawn below

a. What is the initial velocity of the object?

b. What is the maximum velocity?
c. What is the distance travelled by under uniform velocity?
d. What is the deceleration of the object?
e. At which point, the velocity will suddenly become zero?
f. Find the total resultant displacement?
g. What is the total distance travelled by the object?

7. A and B are the objects which move in a same direction. V-t graphs are given below for both
A and B. Initially (when t=0), A leads B by 12.5m.

a. Find the acceleration of B.

b. What is the gap between A and B when t=1 𝑠?
c. What will happen when t=2s?
d. at which point B passes A?
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 e. What is the velocity of B when B passes A?

8. The displacements (s) – time (t) graphs of two objects A and B taken in a straight line are
shown in the graph.

a. How far ahead are A and B in the beginning?

b. Find the velocities in A and B.
c. At what point does B pass A?
d. What are the displacements of A and B in the time taken by B to pass A?
e. By t = 20s, how far ahead is B than A?

9. Two cars, A and B, start from the same place and travel in the same direction on the same
straight line at constant speeds of 50 kmh-1 and 75 kmh-1 respectively. If B started to move 1
hour and 15 minutes after the start of A, find the time it takes for B to pass A and the
displacement of objects that have already taken place, a. Using displacement-time graph.
b. Using velocity-time graph.

10. An object that starts at rest moves first with uniform acceleration, second with a uniform
velocity of 10 ms-1 and the last with uniform deceleration and comes to rest. The total time
taken for the journey is 160s and the displacement is 1.2 km. By using velocity-time graph,
a. Find the distance travelled under uniform velocity.
b. Find the deceleration if the acceleration is 0.5 ms-2.

11. An object moving in a constant deceleration makes a displacement of 200 m in the first two
seconds of its motion. In the next 4s, it makes a displacement of 220 m. Find the velocity at
the end of 7 s from the start of the motion using a velocity time graph.

12. Objects A and B move in the same direction on the same straight line. A moves at a constant
velocity of 11 ms-1. When B is 52.5 m ahead of A, it starts at rest and travels at a constant
acceleration of 1 ms-2. Find the time taken for A to pass B by using velocity-time graph.
Explain the meaning of having two answers.

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13. A 100 m runner who starts motion at rest travels at the first ¾ of motion with 1 ms-2 uniform
acceleration and the last ¼ of the motion, at a constant velocity. By using the velocity-time
graph, find the time it takes him to run the first 50 m and the second 50 m.

Additional notes
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