Selina solutions concise physics class 9 icse Solutions for Chapter 2 chapter 2 motion in one dimension

Exercises in Chapter 2 chapter 2 motion in one dimension Grade 9

Exercise 2A

Exercise 2B

Exercise 2C

Questions in Exercise 2A

State whether the following quantity is a scalar or vector?

(a) Pressure

(b) Force

(d) Energy

(e) Weight

(f) Speed

When is a body said to be at rest?

When is a body said to be in motion?

What do you mean by motion in one direction?

Define displacement. State its unit.

Differentiate between distance and displacement.

Can displacement be zero even if the distance is not zero? Give one example to explain your answer.

When is the magnitude of displacement equal to the distance?

Define velocity. State its unit.

Define speed. What is its S.I. unit?

Distinguish between speed and velocity.

Which of the quantity speed or velocity gives the direction of motion of the body.

When is the instantaneous speed the same as the average speed?

Distinguish between uniform velocity and variable velocity.

Distinguish between average speed and average velocity.

Give an example of the motion of a body moving with a constant speed, but with a variable velocity. Draw a diagram to represent such a motion.

Give an example of motion in which average speed is not zero, but average velocity is zero.

Define acceleration. State its S.I unit.

What is meant by the term retardation? Name its S.I. unit.

Which of the quantity, velocity or acceleration determines the direction of motion?

Give one example of each type of the following motion:

(a) Uniform velocity

(b) Variable velocity

(d) Uniform retardation

The diagram below shows the pattern of the oil on the road, dripping at a constant rate from a moving car. What information do you get from it about the motion of the car?

Define the term acceleration due to gravity. State its average value.

‘The value of g remains the same at all places on the earth surface’. Is this statement true? Give reason for your answer.

If stone and a pencil are dropped simultaneously in a vacuum from the top of a tower, which of the two will reach the ground first? Give reason.

A vector quantity is:

(a) Work

(b) Pressure

(d) Velocity

The S.I. unit of velocity is:

(a) Km h-1

(b) m min-1

(d) m s-1

The unit of retardation is:

(a) $ms^1$

(b) $ms^{-2}$

(d) $ms^{-2}$

A body when projected up with an initial velocity u goes to a maximum height h in time t and then comes back at the point of projection. The correct statement is:

(a) The average velocity is 2h/t

(b) The acceleration is zero

(d) The displacement is zero

$18km h^{-1}$ is equal to:

(a) $10ms^{-1}$

(b) $5 ms^{-1}$

(d) $1.8 ms^{-1 }$

The speed of a car is $72km h^{-1}$ . Express it in $ms^{-1}$ .

Express $15 ms^{-1}$ in $km h^{-1}$ .

Express each of the following in $ms^{-1}$ :

(a) $1km h^{-1}$

(b) $18 km \space min^{-1}$

Arrange the following speeds in increasing order: $10 ms^{-1}$ , $1km \space min^{-1}$ , $18 km h^{-1}$

A train takes 3h to travel from Agra to Delhi with a uniform speed of $65 km h^{-1}$ . Find the distance between the two cities.

A car travels the first 30km with a uniform speed of 60km h-1 and then next 30km with a uniform speed of 40 km h-1. Calculate: (i) the total time of the journey, (ii) the average speed of the car.

A train takes 2h to reach station B from station A, and then 3 h to return from station B to station A. The distance between the two stations are 200km. Find:

(i) The average speed

(ii) The average velocity of the train

A car moving on a straight path covers a distance of 1km due east in 100s. What is (i) the speed and (ii) the velocity of car?

A body starts from rest and acquires a velocity $10 ms^{-1}$ in 2s. Find its acceleration.

A car starting from rest acquires a velocity $180 ms^{-1 }$ in 0.05h. Find the acceleration.

A body is moving vertically upwards. Its velocity changes at a constant rate from 50 m/s to 20 m/s in 3s. What is its acceleration?

A toy car initially moving with a uniform velocity of 18km/h comes to a stop in 2s. Find the retardation of the car in S.I units.

A car accelerates at a rate of $5m/s^2$ . Find the increase in its velocity in 2s.

A car is moving with a velocity 20m/s. The brakes are applied to retard it at a rate of $2m/s^2$ . What will be the velocity after 5s of applying the brakes?

A bicycle initially moving with a velocity 5m/s accelerates for 5s at a rate of $2 m/s^2$ . What will be its final velocity?

A car is moving in a straight line with speed 18km/h. It is stopped in 5s by applying the brakes. Find: (i) the speed of the car in m/s, (ii) the retardation and (iii) the speed of the car after 2s of applying the brakes.

Questions in Exercise 2B

For the motion with uniform velocity, how is the distance travelled related to the time?

What information about the motion of a body is obtained from the displacement-time graph?

(a) What does the slope of a displacement-time graph represent?

(b) Can displacement-time sketch be parallel to the displacement axis? Give a reason for your answer

Draw a displacement-time graph for a boy going to school with a uniform velocity.

State how the velocity-time graph can be used to find (i) the acceleration of a body, (ii) the distance travelled by the body in a given time, and (iii) the displacement of the body in a given time.

What can you say about the nature of the motion of a body if its displacement-time graph is

(a) A straight line parallel to time axis?

(b) A straight line inclined to the time axis with an acute angle?

(d) A curve

The figure shows a displacement-time graph of two vehicles A and B along a straight road. Which vehicle is moving faster? Give reason.

State the type of motion represented by the following sketches in the figure. Give an example of each type of motion.

Draw a velocity-time graph for a body moving with an initial velocity u and uniform acceleration a. Use this graph to find the distance travelled by the body in time t.

What does the slope of the velocity-time graph represent?

The figure shows the velocity-time graph for two cars A and B moving in the same direction. Which car has the greater acceleration? Give a reason for your answer.

Draw the shape of the velocity-time graph for a body moving with (a) uniform velocity, (b) uniform acceleration.

The velocity-time graph for a uniformly retarded body is a straight line inclined to the time axis with an obtuse angle. How is retardation calculated from the velocity-time graph?

The figure shows the displacement-time graph for four bodies A, B, C and D. In each case state what information do you get about the acceleration (zero, positive or negative)?

Draw a graph for acceleration against time for a uniformly accelerated motion. How can it be used to find the change in speed at a certain interval of time?

Draw a velocity-time graph for the free fall of a body under gravity, starting from rest. Take g= $10m/s^2$

How is the distance related with time for the motion under uniform acceleration such as the motion of a freely falling body?

A body falls freely from a certain height. Show graphically the relation between the distance fallen and the square of time. How will you determine g from this graph?

The velocity-time graph of a body in motion is a straight line inclined to the time axis. The correct statement is:

(a) Velocity is uniform

(b) Acceleration is uniform

(d) Neither velocity nor acceleration is uniform

For a uniformly retarded motion, the velocity-time graph is:

(a) A curve

(b) A straight line parallel to the time axis

(d) A straight line inclined to the time axis

For the uniform motion:

(a) The distance-time graph is a straight line parallel to the time axis

(b) The speed-time graph is a straight line inclined to the time axis

(d) The acceleration-time graph is a straight line parallel to the time axis.

The figure shows the displacement-time graph for the motion of a body. Use it to calculate the velocity of the body at t=1s, 2s and 3s, then draw the velocity-time graph for it in figure (b).

The following table gives the displacement of a car at different instants of time.

Time (s)	0	1	2	3	4
Displacment (m)	0	5	10	15	20

(a) Draw the displacement-time sketch and find the average velocity of the car. (b) What will be the displacement of the car at (i) 2.5s and (ii) 4.5s?

A body is moving in a straight line and its displacement at various instants of time is given in the following table:

Time (s)	0	1	2	3	4	5	6	7
Displacment (m)	2	6	12	12	12	18	22	24

Plot displacement-time graph and calculate:

(i) Total distance travelled in interval 1s to 5s,

(ii) Average velocity in time interval 1s to 5s.

The figure shows the displacement of a body at different times.

(a) Calculate the velocity of the body as it moves for time interval (i) 0 to 5s, (ii) 5s to 7s and

(iii) 7s to 9s.

(b) Calculate the average velocity during the time interval 5s to 9s.

[Hint: From 5s to 9s, displacement=7m -3m = 4m]

From the displacement-time graph of a cyclist, given in figure, find:

(i) The average velocity in the first 4s,

(ii) The displacement from the initial position at the end of 10s

(iii) The time after which he reaches the starting point.

The figure ahead represents the displacement-time sketch of motion of two cars A and B. Find:

(i) The distance by which the car B was initially ahead of car A.

(ii) The velocities of car A and car B

(iii) The time in which car A catches car B

(iv) The distance from the start when car A will catch the car B

A body at rest is made to fall from the top of a tower. Its displacement at different instants is given in the following table:

Draw a displacement-time graph and state whether the motion is uniform or non-uniform?

The figure shows the velocity-time graph for the motion of a body. Use it to find the displacement of the body at t=1s, 2s, 3s and 4s, then draw the displacement-time graph for it on figure (b).

The figure below shows a velocity-time graph for a car starting from rest. The graph has three parts AB, BC and CD.

(i) State how is the distance travelled in any part determined from this graph

(ii) Compare the distance travelled in part BC with the distance travelled in part AB.

(iii) Which part of the graph shows motion with uniform (a) Velocity (b) acceleration (c) retardation?

(iv) (a) Is the magnitude of acceleration higher or lower than that of retardation? Give a reason.

(b) Compare the magnitude of acceleration and retardation.

The velocity-time graph of a moving body is given below in figure

Find: (i) The acceleration in parts AB, BC and CD. (ii) Displacement in each part AB, BC, CD, and (iii) Total displacement.

A ball moves on a smooth floor in a straight line with a uniform velocity 10m/s for 6s. At t=6s, the ball hits a wall and comes back along the same line to the starting point with the same speed. Draw the velocity-time graph and use it to find the total distance travelled by the ball and its displacement.

The figure shows the velocity-time graph of a particle moving in a straight line.

(i) State the nature of the motion of a particle.

(ii) Find the displacement of particle at t=6s.

(iii) Does the particle change its direction of motion?

(iv) Compare the distance travelled by the particle from 0 to 4s and from 4s to 6s.

(v) Find the acceleration from 0 to 4s and retardation from 4s to 6s.

Questions in Exercise 2C

Write three equations of uniformly accelerated motion relating the initial velocity (u), final velocity (v), time (t), acceleration (a) and displacement (S).

Derive the following equations for a uniformly accelerated motion: (i) v = u + at (ii) $S=ut+\frac{1}{2}at^2$ (iii) $v^2=u^2+2as$ where the symbols have their usual meanings.

Write an expression for the distance S covered in time T by a body which is initially at rest and starts moving with a constant acceleration a.

The correct equation of motion is:

(a) v = u + 2aS

(b) v = ut + a

(d) v = u + at

A car starting from rest accelerates uniformly to acquire a speed 20km/h in 30 min. The distance travelled by car in this time interval will be:

(a) 600km

(b) 5km

(d) 10km

A body starts from rest with a uniform acceleration of 2m/s. Find the distance covered by the body in 2s.

A body starts with an initial velocity of 10m/s and acceleration $5m/s^2$ . Find the distance covered by it in 5s.

A vehicle is accelerating on a straight road. Its velocity at any instant is 30km/h, after 2s, it is 33.6km/h and after further 2s, it is 37.2km/h. Find the acceleration of the vehicle in $m/s^2$ . Is the acceleration uniform?

A body, initially at rest, starts moving with a constant acceleration $2m/s^2$ . Calculate: (i) the velocity acquired and (ii) and the distance travelled in 5s.

A body initially moving with a velocity 20m/s strikes a target and comes to rest after penetrating a distance 10cm in the target. Calculate the retardation caused by the target.

A train moving with a velocity of 20m/s is brought to rest by applying brakes in 5s. Calculate the retardation.

A train travels with a speed of 60km/h from station A to station B and then comes back with a speed, 80km/h from station B to station A. Find: (i) the average speed, and (ii) the the average velocity of the train.

A train is moving with a velocity of 90km/h. It is brought to stop by applying the brakes which produce retardation of $0.5m/s^2$ . Find: (i) the velocity after 10s, and (ii) the time taken by the train to come to rest.

A car travels a distance 100m with a constant acceleration and average velocity of 20m/s. The final velocity acquired by the car is 25m/s. Find: (i) the initial velocity and (ii) acceleration of car.

When brakes are applied to a bus, the retardation produced is 25cm/s and the bus takes 20s to stop. Calculate: (i) the initial velocity of the bus, and (ii) the distance travelled by bus during this time.

A body moves from rest with uniform acceleration and travels 270m in 3s. Find the velocity of the body at 10s after the start.

A body moving with a constant acceleration travels the distances 3m and 8m respectively in 1s and 2s. Calculate: (i) the initial velocity, and (ii) the acceleration of the body.

A car travels with a uniform velocity of 25m/s for 5s. The brakes are then applied and the car is uniformly retarded and comes to rest in further 10s. Find: (i) the distance which the car travels before the brakes are applied, (ii) the retardation and (iii) the distance travelled by car after applying the brakes.

A spacecraft flying in a straight course with a velocity of 75km/s fires its rocket motors for 6.0s. At the end of this time, its speed is 120km/s in the same direction. Find: (i) spacecraft’s average acceleration while the motors were firing, (ii) the distance travelled by the spacecraft in the first 10s after the rocket motors were started, the motors have been in action for only 6.0s.

A train starts from rest and accelerates uniformly at a rate of 2 $m/s^2$ for 10s. It then maintains a constant speed for 200s. The brakes are then applied and the train is uniformly retarded and comes to rest in the 50s. Find: (i) the maximum velocity reached, (ii) the retardation in the last 50s, (iii) the total distance travelled, and (iv)the average velocity of the train.