Lakhmir Singh & Manjit Kaur: Motion, Solutions- 1

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Q1. Is displacement a scalar quantity ?
Ans: No, displacement is a vector quantity. This means that it has both magnitude and direction, distinguishing it from scalar quantities, which only have magnitude. Understanding this distinction is crucial in physics, as it affects how we analyse motion and forces.

Q2. State whether distance is a scalar or a vector quantity.
Ans: Distance is a scalar quantity. This means it has only magnitude and does not include direction.

Q3. Change the speed of 6 m/s into km/h.
Ans: To convert a speed of 6 m/s into km/h, you can use the following formula:

• Multiply the speed in m/s by 3600 to convert seconds to hours.
• Divide by 1000 to convert meters to kilometres.

The calculation is as follows: 6 m/s = 6 × (3600 / 1000) km/h = 21.6 km/h

Q4. What name is given to the speed in a specified direction ?
Ans: The speed of a body in a specified direction is called velocity.

Q5. Give two examples of bodies having non-uniform motion.
Ans: Examples of bodies exhibiting non-uniform motion include:

• Motion of a bus on a road, where it frequently accelerates and decelerates due to traffic conditions.
• Motion of a racing horse, which varies in speed as it navigates the course and responds to the jockey's commands.

Q6. Name the physical quantity obtained by dividing 'Distance travelled' by 'Time taken' to travel that distance.
Ans: Speed is defined as the distance travelled per unit of time. It represents how quickly an object moves from one point to another and is calculated by dividing the total distance by the total time taken to cover that distance.

Q7. What do the following measure in a car?
(a) Speedometer 
(b) Odometer
Ans: (a) The speedometer of a car measures the instantaneous speed of the vehicle. (b) The odometer is a device used to record the distance travelled by the car.

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Q8. Name the physical quantity which gives us an idea of how slow or fast a body is moving.
Ans: Speed is the physical quantity that indicates how slow or fast a body is moving.

Q9. Under what conditions can a body travel a certain distance and yet its resultant displacement be zero?
Ans: When a body returns to its starting point, it has a resultant displacement of zero, despite covering a certain non-zero distance. This situation occurs during circular or oscillatory motion where the total distance travelled can be significant, yet the net change in position remains unchanged.

Q10. In addition to speed, what else should we know to predict the position of a moving body?
Ans: In addition to speed, we should also know the direction in which the body is moving. Understanding both speed and direction is essential for accurately predicting the position of a moving body.

Q11. When is a body said to have uniform velocity?
Ans: A body is said to have uniform velocity when it covers equal distances in equal intervals of time, regardless of how small or large the time interval may be, and always in a particular direction.

Q12. Under which condition is the magnitude of average velocity equal to average speed?
Ans: The magnitude of average velocity is equal to the average speed when the object moves in a straight line without changing direction. In this case, both quantities measure the same distance covered over time, resulting in equal values.

Q13. Which of the two can be zero under certain conditions: average speed of a moving body or average velocity of a moving body?
Ans: The average velocity of a moving body can indeed be zero under certain conditions. This occurs when the body returns to its initial position after moving, resulting in no overall displacement. In contrast, the average speed is always a non-negative quantity, as it measures the total distance travelled over time without regard to direction. In summary:

• Average Velocity: Can be zero if the initial and final positions are the same.
• Average Speed: Cannot be zero unless the body is stationary.

Q14. Give one example of a situation in which a body has a certain average speed but its average velocity is zero.
Ans: The motion of a boy from his home to the shop (in one direction) and then back home (in the reverse direction) is an example of a situation where a body has a certain average speed but its average velocity is zero.

Q15. What is the acceleration of a body moving with uniform velocity?
Ans: When a body is moving with uniform velocity, its acceleration is zero.

Q16. What is the other name of negative acceleration?
Ans: Negative acceleration is also referred to as retardation.

Q17. Name the physical quantity whose SI unit is :
(a) m/s (b) m/s²
Ans: The physical quantities corresponding to the given SI units are:

• (a)Speed (or Velocity), measured in metres per second (m/s).
• (b)Acceleration, measured in metres per second squared (m/s²).

Q18. What type of motion is exhibited by a freely falling body ?
Ans: The motion exhibited by a freely falling body is known as uniformly accelerated motion. This type of motion occurs when the acceleration remains constant throughout the fall, typically due to the force of gravity acting on the body.

Q19. What is the SI unit of retardation ?
Ans: The SI unit of retardation is metres per second squared (m/s²).

Q20. Fill in the following blanks with suitable words :
(a) Displacement is a........................ quantity whereas distance is a...............................
(b) The physical quantity which gives both, the speed and direction of motion of a body is called its.............................
(c) A motorcycle has a steady................ of 3 m/s². This means that every................... 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
Solution :
(a) vector, scalar
(b) velocity
(c) acceleration, second, velocity, 3m/s
(d) displacement, m/s
(e) velocity, m/s²

Q21. What type of motion, uniform or non-uniform, is exhibited by a freely falling body ? Give reason for your answer.
Ans: A freely falling body exhibits non-uniform motion because it covers smaller distances in the initial 1-second intervals and larger distances in the later 1-second intervals. This means it travels unequal distances in equal intervals of time.

Q22. State whether speed is a scalar or a vector quantity. Give reason for your choice.
Ans: Speed is a scalar quantity because it has magnitude only and does not possess a specified direction.

Q23. Bus X travels a distance of 360 km in 5 hours whereas bus Y travels a distance of 476 km in 7 hours. Which bus travels faster ?
Ans:
For bus X,
Speed= Distance/Time
Speed=360/5=72km/h
For bus Y,
Speed= Distance/Time
Speed=476/7=68 km/h
Speed of bus X is more than that of bus Y. Hence, bus X travels faster.

Q24. Arrange the following speeds in increasing order (keeping the least speed first):

1. An athlete running with a speed of 10 m/s.
2. A bicycle moving with a speed of 200 m/min.
3. A scooter moving with a speed of 30 km/h.

Ans:
Speed of athelete = 10 m/s
Speed of bicycle = 200 m/min = 200/60 m/s = 3.33 m/s
Speed of scooter = 30 km/h = 30000/3600 m/s = 8.33 m/s
3.33 m/s < 8.33 m/s < 10 m/s
i.e. 200 m/min < 30 km/h < 10 m/s

Q25. (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.
Solution :

(b) u = 0 m/s

v = 21m/s

Time, t =  1 min = 60 sec

Q26. (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.
Ans:
(a) Acceleration
(b) Retardation
(c) No, because if a body takes a round trip such that its final position is same as the starting position, then the displacement of the body is zero but the distance travelled is non-zero.

Q27. A snail covers a distance of 100 metres in 50 hours. Calculate the average speed of snail in km/h.

​

Ans:
Average speed = Total distance travelled/ Total time taken
Total distance travelled = 100m = 0.1 km; Total time taken = 50 hr
Average speed = 0.1/50 = 0.002km/h 

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Question 28:
A tortoise moves a distance of 100 metres in 15 minutes. What is the average speed of tortoise in km/h ?
Solution :
Total distance=100m =0.1 km
Total time taken=15 minutes= 15/60=0.25 hour
Average speed = Total distance travelled/ Total time taken
=0.1/0.25= 0.4km/h

Question 29:
If a sprinter runs a distance of 100 metres in 9.83 seconds, calculate his average speed in km/h.
Solution :
Total distance travelled =100m
Total time taken = 9.83 sec
Average speed = Total distance travelled/ Total time taken
=100/9.83 =10.172m/s
Averge speed in km/h:
10.172 x(3600/1000)=36.62 km/h

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.

Solution :

Speed from A to B = 30 km/h

Let the distance from A to B be D,

Time taken to travel from A to B, 

Speed from B to A = 20 km/h

Time taken to travel from B to A, T₂ = 

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 ?
Solution :
Initial velocity= 0m/s
Final velocity=6m/s
Time=3 sec
Initial Velocity = 0 m/s

Final Velocity = 6 m/s

Time = 3 Sec

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' ?
Solution :
Initial velocity, u = 600 km/h
Final velocity, v = 1100 km/h
Acceleration = 10 km/h/s = 600 km/h²
From relation, a = (v-u)/t
t = (v-u)/a
t = (1100-600)/600 = 500/600 = 5/6 hr = 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 ?
Solution :
Deceleration, a=-5m/s²
Initial velocity, u=20m/s
Final velocity, v=0m/s
t=?

Deceleration, a = -5m/s²

Initial Velocity, u = 20m/s 

Final Velocity, v = 0 m/s

Question 34:
(a) What is the difference between 'distance travelled' by a body and its 'displacement' ? Explain with the
help of a 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.
Solution :
(a) Distance travelled is the actual length of the indirect path covered by the body whereas displacement refers to the straight line path between the initial and final positions. For e.g. In the figure given below, a body moves from point A to point B and then from point B to point C. Here, the distance travelled by the body is AB + BC and displacement is AC. 

PQ = 8cm

QR = 6 cm

Resultant Displacement PR = 

Question 35:
Define motion. What do you understand by the terms 'uniform motion' and 'non-uniform motion' ? Explain with examples.
(a) Define speed. What is the SI unit of speed ?
(b) What is meant by (i) average speed, and (ii) uniform speed ?
Solution :
A body is said to be in motion when its position changes continuously with respect to a stationary object taken as reference point.
A body has uniform motion if it travels equal distances in equal intervals of time, no matter how small these time intervals may be. For example: a car running at a constant speed of 10m/s, will cover equal distance of 10m every second, so its motion will be uniform.
Non-uniform motion: A body has a non-uniform motion if it travels unequal distances in equal intervals of time. For example: dropping a ball from the roof of a tall building . 

Question 36:
(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.
Solution :
(a) Speed of a body is the distance travelled by it per unit time. The SI unit of speed is m/s.
(b) (i) Average speed of a body is the total distance travelled divided by the total time taken to cover this distance.
(ii) Uniform speed refers to the constant speed of a moving body. A body has a uniform speed if it travels equal distance in equal intervals of time, no matter how small these time intervals may be. 

(a) Speed of the body is the distance travelled by it per unit time. The SI unit of speed is m/s.

(b) (i) Average speed of a body is the total distance travelled divided by the total time taken to cover the distance.

(ii) Uniform speed refers to the constant speed of a moving body.  A body has a uniform speed if it travels equal distance in equal intervals of time, no matter how small these time interval may be.

Question 37:
(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.
Solution :
(a) Velocity of a body is the distance travelled by it per unit time in a given direction. SI unit of velocity is m/s.
( b)(i)Speed is a scalar quantity whereas velocity is a vector quantity.
(ii) Speed of a body is distance travelled by it per unit time whereas velocity of a body is the distance travelled by it per unit time in a given direction.
(iii)Speed is always positive whereas velocity can be both positive as well as negative.
(c) Speed = 54km/h = 54 x (1000/3600) = 15m/s  

Question 38:
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 ?
Solution :
(a) Acceleration of a body is defined as the rate of change of its velocity with time. SI 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: Motion of a freely falling body.  

Question 39:
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. 

Solution : 

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.
Solution : 

(i) In the first part, train travels at a speed of 30 km/h for a distance of 15 km.

(ii) In the second part, train travel at a speed of 50 km/h for a distance of 75 km

(iii) in the third part, train travel at a speed of 20 km/h for a distance of 10 km

Total distance covered  = 15+75+10 = 100km

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 ?
Solution : 

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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 ?
Solution :
Distance travelled in half a rotation of a circular path is equal to the circumference of semi-circle, i.e.,

Distance travelled in half of a circular path is equal to the circumference of semi-circle, i.e = πR.

Displacement = diameter of circle = 2R

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 ?
Solution :
(i) Distance travelled = 6 km
(ii) Displacement = zero(since final position is same as initial position)

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 ?
Solution :
(i) Total distance travelled= 3 + 4 +9=16 km
(ii) The body travels a total distance of 12 km in east direction i.e. towards x-axis.
And it travels a distance of 4 km in North direction, i.e. towards y-axis. Hence, resultant displacement is

(i) Total distance travelled  = 3+4+9 = 16 km

(ii) The body travel a total distance of 12 km in east direction i.e toward  x-axis

And it travel a distance of 4 km in North direction, i.e toward  y- axis

Hence, resultant displacement is

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.
Solution :
(a) Total distance covered in going to the bookshop and coming back to the classroom = 20 + 20 = 40m
Total time taken= 25 + 25 = 50 sec 

(a) total distance covered in going to the bookshop and coming back to the classrooom = 20+20 = 40 km

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.
Solution :
In the first case, car travels at a speed of 60 km/h for a distance of 100 km
In the second case, car travels at a speed of 40 km/h for a distance of 100 km
Total distance travelled = 200 km 

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

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

Total distance travelled  = 200 km

Average speed=

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 ?
Solution :
Initial velocity, u=6m/s
Final velocity ,v=-4.4m/s(the ball rebounds in opposite direction)
Time, t = 0.040 s