#### Question 1:

Is displacement a scalar quantity?

No, displacement is a vector quantity because it has magnitude as well as direction.

#### Question 2:

State whether distance is a scalar or a vector quantity.

Distance is a scalar quantity; it has magnitude but no specific direction.

#### Question 3:

Change the speed of 6 m/s into km/h.

We have to convert 6 m/s into km/h. So,

#### Question 4:

What name is given to the speed in a specified direction?

Velocity is the name given to the speed of a body in a particular direction.

#### Question 5:

Give two examples of bodies having non-uniform motion.

Two examples of non-uniform motion:
(a) Motion of a bus on a curved road
(b) Motion of a bee flying randomly in air.

#### Question 6:

Name the physical quantity obtained by dividing 'Distance travelled' by 'Time taken' to travel that distance.

Speed is obtained by dividing 'distance travelled' by 'time taken' to travel that distance.

#### Question 7:

What do the following measure in a car?

(a) Speedometer
(b) Odometer

(a) Speedometer of a car is used to measure the instantaneous speed of the car.
(b) Odometer of a car is used to record and measure the overall distance travelled by the car.

#### Question 8:

Name the physical quantity which gives us an idea of how slow or fast a body is moving.

Speed is the physical quantity that gives the idea of how slow or fast a body is moving.

#### Question 9:

Under what conditions can a body travel a certain distance and yet its resultant displacement be zero?

When the body comes back to its starting point, its resultant displacement is zero. It is because it has covered a certain distance in due course of time; however, there is no difference between the initial and final positions.

#### Question 10:

In addition to speed, what else should we know to predict the position of a moving body?

Besides speed, we should know the direction to predict the position of a moving body.

#### Question 11:

When is a body said to have uniform velocity?

When a body covers equal distances in equal intervals of time in a particular direction, it is said to have uniform velocity.

#### Question 12:

Under which condition is the magnitude of average velocity equal to average speed?

The magnitude of average velocity is equal to average speed when an object covers equal distances in equal intervals of time in a particular direction.

#### Question 13:

Which of the two can be zero under certain conditions : average speed of a moving body or average velocity of a moving body?

Average velocity of a moving body can be zero. This is because the net displacement for a given time interval can be zero.

#### Question 14:

Give one example of a situation in which a body has a certain average speed but its average velocity is zero.

Motion of a boy from his home to shop and back to home is an example of a situation in which a body has a certain average speed but its average velocity is zero.

#### Question 15:

What is the acceleration of a body moving with uniform velocity?

The acceleration of a body moving with uniform velocity is zero.

#### Question 16:

What is the other name of negative acceleration?

Retardation is the other name for negative acceleration.

#### Question 17:

Name the physical quantity whose SI unit is :

(a) m/s
(b) m/s2

(a) Speed or velocity is expressed in m/s.
(b) Acceleration or retardation is expressed in m/s2.

#### Question 18:

What type of motion is exhibited by a freely falling body?

A freely falling body exhibits uniform accelerated motion.

#### Question 19:

What is the SI unit of retardation?

The S.I. unit of retardation is m/s2.

#### Question 20:

(a) Displacement is a __________ quantity, whereas distance is a __________ quantity.
(b) The physical quantity that includes both the speed and direction of the motion of a body is called its __________.
(c) A motorcycle has a steady __________ of 3 m/s2. This means that each __________ its __________ increases by __________.
(d) Velocity is the rate of change of __________. It is measured in __________.
(e) Acceleration is the rate of change of __________. It is measured in __________.

(a) Displacement is a vector quantity, whereas distance is a scalar quantity.
(b) The physical quantity that includes both the speed and direction of the motion of a body is called its velocity.
(c) A motorcycle has a steady acceleration of 3 m/s2. This means that each second its velocity increases by 3 m/s.
(d) Velocity is the rate of change of displacement. It is measured in m/s.
(e) Acceleration is the rate of change of velocity. It is measured in m/s2.

#### Question 21:

What type of motion, uniform or non-uniform, is exhibited by a freely falling body? Give reason for you answer.

A freely falling body exhibits non-uniform motion. Its velocity increases at a constant rate, so it shows uniformly accelerated motion.

#### Question 22:

State whether speed is a scalar or a vector quantity. Give reason for your choice.

Speed is a scalar quantity. This is because it has magnitude, but it does not specify direction. It is the distance travelled by a body per unit time.

#### Question 23:

Bus X travels a distance of 360 km in 5 hours whereas bus Y travels a distance of 476 km in hours. Which bus travels faster?

We should first consider Bus X.
Distance travelled (d1) = 360 km
Time taken (d1) = 5 hr
So, we can calculate the speed as:

Thus, the speed of Bus X is 72 km/h.
Similarly,
For Bus Y:
Distance travelled
Time taken (t2) = 7 hr
So, we can calculate the speed as:

Thus, the speed of Bus Y is 68 km/h.
Speed of Bus X is more than that of Bus Y. Hence, Bus X travels faster.

#### Question 24:

Arrange the following speeds in increasing order (keeping the least speed first):

(i) An athlete running with a speed of 10 m/s.
(ii) A bicycle moving with a speed of 200 m/min.
(iii) A scooter moving with a speed of 30 km/h.

We have three different moving bodies. To compare their speeds, we need to express them in similar S.I. units.
(i) An athlete running with a speed of 10 m/s.
(ii) A bicycle moving with a speed of 200 m/min. Converting into S.I. units, the speed will be:

(iii) A scooter moving with a speed of 30 km/h. Converting into S.I. units, the speed will be:

On arranging the speeds in ascending order, we get:
(ii) < (iii) < (i)

#### Question 25:

(a) Write the formula for acceleration. Give the meaning of each symbol which occurs in it.
(b) A train starting from Railway Station attains a speed of 21 m/s in one minute. Find its acceleration.

(a) Acceleration is the change in velocity per unit time; it is a vector quantity.

The above expression can also be written as:

Where,
a = Acceleration
= Final velocity
= Initial velocity
= Time taken

(b) We will find the value of uniform acceleration.
Initial velocity (u) 0 m/s
Final velocity (v) = 21 m/s
Time taken (t) = 60 s
Acceleration:
$a\mathit{=}\frac{v\mathit{-}u}{t}$
Putting the values in the above equation, we get:


#### Question 26:

(a) What term is used to denote the change of velocity with time?
(b) Give one word which means the same as 'moving with a negative acceleration'.
(c) The displacement of a moving object in a given interval of time is zero. Would the distance travelled by the object also be zero? Give reason for your answer.

(a) Acceleration is used to denote the change in velocity with time.
(b) Retardation is the same as ‘moving with a negative acceleration'.
(c) Displacement is a vector quantity, so it can be zero for two reasons:
1. When the body doesn't move at all: In this case, the distance travelled will also be zero.
2. When the body comes back to its initial position: In this case, the distance travelled is non-zero, but the displacement is zero.

#### Question 27:

A snail covers a distance of 100 metres in 50 hours. Calculate the average speed of snail in km/h.

Figure

Distance (d) = 1000 m = 0.1 km
Time (t) = 50 hr
So, we can calculate the speed as:

Average speed for the entire journey:

#### Question 28:

A tortoise moves a distance of 100 metres in 15 minutes. What is the average speed of tortoise in km/h?

Distance (d) = 0.1 km

So, we can calculate the speed as:

Average speed for the entire journey:

#### Question 29:

If a sprinter runs a distance of 100 metres in 9.83 seconds, calculate his average speed in km/h.

Distance (d) = 100 m
Time (t) = 9.83 s
So, we can calculate the speed as:

Average speed for the entire journey:

Now, we can convert it in km/h as:

#### Question 30:

A motorcyclist drives from place A to B with a uniform speed of 30 km h−1 and returns from place B to A with a uniform speed of 20 km h−1. Find his average speed.

We have to find the average velocity of the entire journey. For this, we have the following information:
Speed from A to B = (v1) = 30 m/s
Let the distance from A to B be  (d).
Also, let the time taken to travel from A to B be (t1).

We have:
${t}_{1}=\frac{d}{30}$
Speed from B to A (v2) = 20 m/s
Let the time taken to travel from B to A be(t2).
Thus, we have:

Total distance travelled is 2d.
Therefore,

On putting the values to obtain the average speed of the motorcyclist, we get:

#### Question 31:

A motorcyclist starts from rest and reaches a speed of 6 m/s after travelling with uniform acceleration for 3 s. What is his acceleration?

We have to find the value of uniform acceleration.
Initial velocity (u) = 0 m/s
Final velocity (v) = 6 m/s
Time taken (t) = 3s
Acceleration:

Put the values in the above equation to obtain the value of acceleration.

#### Question 32:

An aircraft travelling at 600 km/h accelerates steadily at 10 km/h per second. Taking the speed of sound as 1100 km/h at the aircraft's altitude, how long will it take to reach the 'sound barrier'?

Final velocity, v = 1100 km/h = 1100 × 5/18 = 305.55 m/s
Initial velocity, u = 600 km/h = 600 × 5/18 = 166.66 m/s
Acceleration = 10 km/h per second = 10 × 5/18 = 2.77 m/s2
Time taken by body,
v = u + at
t = (v - u)/a
t  = (305.55 -166.66 )/2.77
t = 50.14 sec
t ≃ 50 sec

#### Question 33:

If a bus travelling at 20 m/s is subjected to a steady deceleration of 5 m/s2, how long will it take to come to rest?

We have to find the time taken to reach the given final velocity.
We have:
Initial velocity (u) = 20 m/s
Final velocity  (v) = 0 m/s
Acceleration for the entire journey (a) = –5 ms2.
Let the time taken be (t).
We can calculate the time taken using the first equation of motion.

Time taken by the bus to come to rest:

#### Question 34:

(a) What is the difference between 'distance travelled' by a body and its 'displacement'? Explain with the help of diagram.
(b) An ant travels a distance of 8 cm from P to Q and then moves a distance of 6 cm at right angles to PQ. Find its resultant displacement.

(a)

 Distance Displacement 1. Distance has only magnitude, with no specified direction. 1. Displacement has magnitude as well as direction. 2. It is a scalar quantity. 2. It is a vector quantity. 3. Two different distances can be added directly. 3. We have to follow the vector addition method to add displacements.

One difference in diagrammatic form is as follows:

Here the curved line is the distance traveled and the straight line is the magnitude of the displacement.

(b) We have to find the resultant displacement from the given diagram:

We have:
PQ = 8 cm and QR = 6 cm
Resultant displacement:

The direction of this displacement is from P to R. If θ is the angle made by PR with PQ then,'

This is the angle made by the resultant with PQ.

#### Question 35:

Define motion. What do you understand by the terms 'uniform motion' and 'non-uniform motion'? Explain with examples.

A body is said to be in motion when its position changes continuously with respect to a stationary point taken as the reference point.

Uniform motion: A body is said to be in uniform motion if it travels equal distances in equal intervals of time in a particular direction, no matter how small these time intervals are.
For example, a car running at a constant speed of 10 m/s towards east will cover the equal distance of 10 m every second towards east, so its motion will be uniform.

Non-uniform motion: A body is said to be in non-uniform motion if it travels unequal distances in equal intervals of time.
For example, motion of a freely falling ball from the roof of a tall building.

#### Question 36:

(a) Define speed. What is the SI unit of speed?
(b) What is meant by (i) average speed, and (ii) uniform speed?

(a) Speed of a body is the distance travelled by it per unit time. The S.I. unit of speed is m/s.
(b) (i) Average speed of a body is the total distance travelled by it divided by the total time taken by it to cover the given distance.

(ii) A body has a uniform speed if it travels equal distance in equal intervals of time, no matter how small these time intervals are.

#### Question 37:

(a) Define velocity. What is the SI unit of velocity?
(b) What is the difference between speed and velocity?
(c) Convert a speed of 54 km/h into m/s.

(a) Velocity of a body is the distance travelled by it per unit time in a given direction. The S.I. unit of velocity is m/s. It is a vector quantity.

(b) (i) Speed is a scalar quantity, whereas velocity is a vector quantity.
(ii) Speed of a body is the distance travelled by it per unit time, whereas the velocity of a body is the distance travelled by it per unit time in a given direction.
(iii) Speed is always positive, while velocity can be both positive and negative, depending upon the direction.

(c) We have to convert 54 km/h into m/s.

#### Question 38:

(a) What is meant by the term 'acceleration'? State the SI unit of acceleration.
(b) Define the term 'uniform acceleration'. Give one example of a uniformly accelerated motion.

(a) Acceleration of a body is defined as the rate of change of its velocity with respect to time. It is a vector quantity.    The S.I. unit of acceleration is  (m/s2) .
(b) A body has uniform acceleration if it travels in a straight line and its velocity increases by equal amounts in equal intervals of time.
For example, a freely falling body has uniform acceleration.

#### Question 39:

The distance between Delhi and Agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. How fast must the train travel the next 100 km, so as to average 70 km/h for the whole journey?

We have the following data to find the speed for the second part of the journey:
Total distance to be travelled by train (D) = 200 km
Average speed required (vavg) = 70 km/hr
Time required for the entire journey (T):

For the first part of the trip:
Distance covered (d1) = 100 km
Speed for this part of journey (v1) = 50 km/hr
Time taken for the first part of journey:

For the second part of the trip,
Distance covered (d2) = 100 km
Time taken for the second part of journey:

Speed of the train for the second part of the journey:

#### Question 40:

A train travels the first 15 km at a uniform speed of 30 km/h; the next 75 km at a uniform speed of 50 km/h; and the last 10 km at a uniform speed of 20 km/h. Calculate the average speed for the entire train journey.

(i) In the first case, the train travels at a speed of 30 km/h for a distance of 15 km.
We can find the time as:

(ii) In the second case, the train travels at a speed of 50 km/h for a distance of 75 km.
We can find the time as:

(iii) In the third case, the train travels at a speed of 20 km/h for a distance of 10 km.
We can find the time as:

Total distance covered:
= (15 + 75 + 10) km
= 100 km
Total time taken = (0.5 + 1.5 + 0.5) km
= 2.5
Therefore,
Now, put the values to get the average speed.

#### Question 41:

A car is moving along a straight road at a steady speed. It travels 150 m in 5 seconds:

(a) What is its average speed?
(b) How far does it travel in 1 second?
(c) How far does it travel in 6 seconds?
(d) How long does it take to travel 240 m?

(a) We have:
Distance (d) = 150 m
Time (t) = 5s
So, we can calculate average the speed as:

Average speed for the entire journey:

(b) We have to calculate the distance travelled in 1s.
Distance = (Speed) (Time)
Distance travelled in one second:
=(30) (1) m

(c) We have to calculate the distance travelled in 6 s.
Distance = (Speed) (Time)
Distance travelled in one second:
= (30) (6) m

(d) We have:
Distance (d) = 240 m
Speed (v) = 30 m/s
We can find the time as:

#### Question 42:

A particle is moving in a circular path of radius r. The displacement after half a circle would be:

(a) 0
(b) πr
(c) 2r
(d) 2πr

(c) Displacement is the difference between the final and initial position of a body. It is a vector quantity and is independent of the path taken. So, for the movement of half of a circle, the displacement is 2r, where r is the radius of the circular path.

#### Question 43:

The numerical ratio of displacement to distance for a moving object is :

(a) always less than 1
(b) equal to 1 or more than 1
(c) always more than 1
(d) equal to 1 or less than 1

(d), i.e., Equal to 1 or less than 1.
Displacement is always smaller than or equal to displacement.

#### Question 44:

A boy is sitting on a merry-go-round which is moving with a constant speed of 10 m s−1. This means that the boy is :

(a) at rest
(b) moving with no acceleration
(c) in accelerated motion
(d) moving with uniform velocity

(c) Acceleration is the rate of change of velocity, and the velocity of the merry-go-round is changing with respect to time. Thus, it will move in an accelerated motion.

#### Question 45:

In which of the following cases of motion, the distance moved and the magnitude of displacement are equal?

(a) if the car is moving on straight road
(b) if the car is moving on circular road
(c) if the pendulum is moving to and fro
(d) if a planet is moving around the sun

(a) The magnitude of displacement is equal to the distance travelled by a body when it travels in a straight line.

#### Question 46:

The speed of a moving object is determined to be 0.06 m/s. This speed is equal to :

(a) 2.16 km/h
(b) 1.08 km/h
(c) 0.216 km/h
(d) 0.0216 km/h

(c) We can convert 0.06 m/s as:

So, the answer is 0.216 km/h.

#### Question 47:

A freely falling object travels 4.9 m in 1st second, 14.7 m in 2 nd second, 24.5 m in 3rd second, and so on. This data shows that the motion of a freely falling object is a case of :

(a) uniform motion
(b) uniform acceleration
(c) no acceleration
(d) uniform velocity

(b) The displacement of the body in equal interval of time is unequal, but acceleration is constant. The acceleration will thus be uniform, so the answer is (b).

#### Question 48:

When a car runs on a circular track with a uniform speed, its velocity is said to be changing. This is because :

(a) the car has a uniform acceleration
(b) the direction of car varies continuously
(c) the car travels unequal time intervals.
(d) the car travels equal distances in unequal time intervals

(d) When a car runs on a circular track, its velocity changes continuously, as its direction keeps changing.

#### Question 49:

Which of the following statement is correct regarding velocity and speed of a moving body?

(a) velocity of a moving body is always higher than its speed
(b) speed of a moving body is always higher than its velocity
(c) speed of a moving body is its velocity in a given direction
(d) velocity of a moving body is its speed in a given direction

(d) Velocity is a vector quantity having a magnitude and a specific direction. So, velocity is nothing but speed in a particular direction.

#### Question 50:

Which of the following can sometimes be 'zero' for a moving body?

(i) average velocity
(a) only (i)

(ii) distance travelled
(b) (i) and (ii)

(iii) average speed
(c) (i) and (iv)

(iv) displacement
(d) only (iv)

(c) Distance is the length of the actual path covered by a moving body. This implies that the distance travelled by a moving body and also its average speed can never be zero at any point of time. However, it is possible for the displacement as well as average velocity for the body to be zero at an instance during the motion of the particle.

#### Question 51:

When a car driver travelling at a speed of 10 m/s applies brakes and brings the car to rest in 20 s, then retardation will be:

(a) + 2 m/s2
(b) − 2 m/s2
(c) − 0.5 m/s2
(d) + 0.5 m/s2

(d) The term “retardation” means negative acceleration.
Initial velocity = 10 m/s
Final velocity = 0 m/s
Time taken = 20 s

#### Question 52:

Which of the following could not be a unit of speed?

(a) km/h
(b) s/m
(c) m/s
(d) mm s−1

(b) Speed is the distance travelled by a moving body per unit time.

#### Question 53:

One of the following is not a vector quantity. This one is :

(a) displacement
(b) speed
(c) acceleration
(d) velocity

(b) Vector quantities have magnitude as well as direction, and they obey the laws of vector addition.

#### Question 54:

Which of the following could not be a unit of acceleration?

(a) km/s2
(b) cm s−2
(c) km/s
(d) m/s2

(c) Acceleration is defined as the rate of change of velocity.

#### Question 55:

A body is moving along a circular path of radius R. What will be the distance travelled and displacement of the body when it completes half a revolution?

We have to analyse the distance and displacement of a body that has covered half the perimeter of a circle.
Distance travelled in half a rotation of a circular path is equal to the circumference of semi-circle.
Distance travelled = πR
Displacement is calculated from the initial and final positions of a body. It is independent of the path covered. So, displacement is the diameter of the semi-circle.
Hence, displacement is 2R, where R is the radius of the circular path.

#### Question 56:

If on a round trip you travel 6 km and then arrive back home :

(a) What distance have you travelled?
(b) What is your final displacement?

(a) Distance travelled is the actual path covered.
Total distance covered in this case due to going and coming back:
2d = 6 km
is the distance of one-side journey.

(b) Displacement is calculated from the initial and final positions of a body. It is independent of the path covered. So, displacement in this case is 0 because the initial and final positions are the same.

#### Question 57:

A body travels a distance of 3 km towards East, then 4 km towards North and finally 9 km towards East.
(i) What is the total distance travelled?
(ii) What is the resultant displacement?

1-22-57
(i) Distance travelled is the actual path covered.
Total distance travelled:
= (3 + 4 + 9) km
= 16 km

(ii) The body travels a total distance of 12 km east, which means towards the x-axis, on a Cartesian plane. It travels a distance of 4 km in north direction, which means towards y-axis.
Resultant displacement:

#### Question 58:

A boy walks from his classroom to the bookshop along a straight corridor towards North. He covers a distance of 20 m in 25 seconds to reach the bookshop. After buying a book, he travels the same distance in the same time to reach back in the classroom. Find (a) average speed, and (b) average velocity, of the boy.

(a)    Distance travelled is the length of the actual path covered.
Total distance covered in going and coming back:
= (20 + 20) m
= 40 m
Total time taken, = (25 + 25) s
= 50 s
So, we can calculate average speed as:

Average speed for the entire journey:

(b) Average velocity is zero, as displacement is zero because the boy arrives at the initial point.

#### Question 59:

A car travels 100 km at a speed of 60 km/h and returns with a speed of 40 km/h. Calculate the average speed for the whole journey.

In the first case, the car travels at a speed of 60 km/h for a distance of 100 km.
Thus,

In the second case, the car travels at a speed of 40 km/h for a distance of 100 km.
Thus,

Total time taken:

Total distance travelled = 200 km
We can calculate average speed as:

Average speed for the entire journey:

#### Question 60:

A ball hits a wall horizontally at 6.0 m s−1. It rebounds horizontally at 4.4 m s−1. The ball is in contact with the wall for 0.040 s. What is the acceleration of the ball?

We have to find the value of uniform acceleration.
We have:
Initial velocity (u) = 6 m/s
Final velocity is in opposite direction to that of initial velocity (v) = –4.4 m/s
Time taken (t) = 0.04 s
Acceleration:

Put the values in the above equation to get the value of acceleration.