## Std 9 Science Chapter 1 Laws of Motion Exercise

**1. Match the first column with appropriate entries in the second and third columns and remake the table.**

SR.NO | Column 1 | Column 2 | Column 3 |

1 | Negative acceleration | The velocity of observation remains constant | A car, initially at rest reaches a velocity of 50 km/hr in 10 seconds. |

2 | Positive acceleration | The velocity of the object decreases. | A vehicle is moving with a velocity of 25 m/s |

3 | Zero accerleration | The velocity of the object increases | A vehicle moving with the velocity of 10 m/s, stops after 5 seconds |

**ANSWERS**

SR.NO | Column 1 | Column 2 | Column 3 |

1 | Negative acceleration | The velocity of the object decreases. | A vehicle moving with the velocity of 10 m/s, stops after 5 seconds |

2 | Positive acceleration | The velocity of the object increases | A car, initially at rest reaches a velocity of 50 km/hr in 10 seconds. |

3 | Zero accerleration | The velocity of the object remains constant | A vehicle is moving with a velocity of 25 m/s. |

**2. Clarify the differences**

**A. Distance and displacement**

Distance | Displacement |

‘Distance’ is the length of the actual path travelled by an object in motion while going from one point to another. | Displacement is the minimum distance between the starting and finishing points. |

Distance is a scalar quantity | Displacement is a vector quantity |

It is always positive | It may be negative, positive or zero. |

It is either equal to or greater than displacement. | It is either equal to or less than distance. |

**B. Uniform and non-uniform motion.**

Uniform motion | Non-uniform motion |

An object in uniform motion covers equal distances in equal time intervals. | An object in non-uniform motion covers unequal distances in equal time intervals. |

Distance-time graph for uniform motion is a straight line | Distance-time graph for uniform motion is not a straight line. |

Acceleration is zero | Acceleration is non-zero |

**3. Complete the following table. **

u (m/s) | a (m/s2 ) | t (sec) | v = u + at (m/s) |

2 | 4 | 3 | 14 |

10 | 5 | 2 | 20 |

v = u + at (m/s)

= 2 + 4 x 3

= 2 + 12

= 14 m/s

v = u + at (m/s)

= 10 + 5 x 2

= 10 + 10

= 20 m/s

u (m/s) | a (m/s^{2} ) | t (sec) | s = ut + ½ at^{2} (m) |

5 | 12 | 3 | 69 |

7 | 8 | 4 | 92 |

s = ut + ½ at^{2}

= 5 x 3 + ½ x 12 x 3^{2}

= 15 + ½ x 12 x 3 x 3

= 15 + 54

= 69 m

s = ut + ½ at^{2}

= 7 x 4 + ½ x 8 x 4^{2}

= 28 + ½ x 8 x 4 x 4

= 28 + 64

= 92 m

u(m/s) | a(m/s^{2} ) | s(m) | v ^{2} = u ^{2} + 2as (m/s)^{2} |

4 | 3 | 8 | 8 |

4 | 5 | 8.4 | 10 |

v ^{2} = u ^{2} + 2as

= 4^{2} + 2 x 3 x 8

= 16 + 48

= 64

v = 8 (m/s)^{2}

v ^{2} = u ^{2} + 2as

= 4^{2} + 2 x 5 x 8.4

= 16 + 84

= 100

v = 10 (m/s)^{2}

**4. Complete the sentences and explain them.**

a. The minimum distance between the start and finish points of the motion of an object is called the **displacement** of the object.

b. Deceleration is **negative** acceleration.

c. When an object is in uniform circular motion, its **direction** changes at every point.

d. During collision **total momentum** remains constant.

e. The working of a rocket depends on Newton’s **Third** law of motion.

**5. Give scientific reasons. **

**a. When an object falls freely to the ground, its acceleration is uniform. **

ANS: 1. When the body falls freely on the ground, there are equal changes in velocity of body in equal intervals of time.

2. Thus the acceleration of the body is constant.

3. Hence, its acceleration is uniform.

**b. Even though the magnitudes of action force and reaction force are equal and their directions are opposite, their effects do not get cancelled. **

ANS: 1. Reaction and action forces act on different bodies.

2. They cannot cancel each others effect as they do not act on the same body.

3. Hence, Even though the magnitudes of action force and reaction force are equal, they do not cancel each other.

**c. It is easier to stop a tennis ball as compared to a cricket ball, when both are travelling with the same velocity.**

ANS: 1. Momentum of an object depends on its velocity as well as its mass.

2. Cricket ball is heavier than a tennis ball. Although they are thrown with the same velocity, cricket ball has more momentum velocity then the tennis ball.

3. Hence, to stop the cricket ball more force is required.

4. Hence, It is easier to stop a tennis ball than a cricket ball moving with same velocity.

**d. The velocity of an object at rest is considered to be uniform.**

ANS: 1. When a body is in a state of rest, it attains a constant velocity.

2. A body with the constant velocity is said to be in uniform motion.

3. Hence, The velocity of an object at rest is an example of uniform motion.

**6. Take 5 examples from your surroundings and give explanation based on Newtons laws of motion. **

ANS: 1) When a ball is kicked in space, the ball keeps moving in one direction as there is no gravity. The ball stops when it hits an object or pulled by other planet’s gravity.

2) When a fast moving car is hit by some object, like a tree, the car immediately stops but continues to move forward. Airbags are provided to safeguard the driver.

3) Considering that the same amount of force is used to move a car and a truck, the car will move faster than the truck, because car has less mass.

4) To push an empty shopping cart is easy than pushing a cart that is full. This is because, the fully loaded cart is heavy as it has more mass which requires more force to push the cart.

5) Releasing air from the balloon causes the balloon to file up. Thus the opposite reaction.

**7. Solve the following examples. **

**a) An object moves 18 m in the first 3 s, 22 m in the next 3 s and 14 m in the last 3 s. What is its average speed? **

**Given**: Total distance (d) = 18 + 22 + 14 = 54 m

Total time taken (t) = 3 + 3 + 3 = 9 sec

**To find:** Average speed =?

Formula: Average speed = Total distance covered/Total time taken

**Solution** : Average speed = Total distance covered / Total time taken

= 54/ 9

= 6 m/s

** Ans:** The object moves with an average speed of 6 m/s.

**b) An object of mass 16 kg is moving with an acceleration of 3 m/s2 . Calculate the applied force. If the same force is applied on an object of mass 24 kg, how much will be the acceleration? **

**Given :**

Mass of 1st body (m_{1}) = 16 kg

Acceleration of 1st body (a_{1}) =
3 m/s^{2}

Mass of 2nd body (m^{2}) = 24 kg

**To find:** Force on 1st body (F1) =?

Acceleration of 2nd body (a_{2}) =?

Formula: F = m · a

**Solution:**

F_{1}
= m_{1} · a_{1}

F_{1} = 16 × 3

F_{1}
= 48 N

a_{2} = F_{2} / m_{2}

a_{2 = }48 / 24

a_{2} = 2m/s^{2 }

**Ans:** The force acting on the 1^{st }body is 48 N and the acceleration of the 2^{nd} body is 2 m/s^{2}

**c) A bullet having a mass of 10 g and moving with a speed of 1.5 m/s, penetrates a thick wooden plank of mass 90 g. The plank was initially at rest. The bullet gets embedded in the plank and both move together. Determine their velocity. **

**Given:** Mass of bullet (m_{1}) = 10 g = 10/1000 kg = 0.010 kg Mass of plank (m_{2}) = 90 g = 0.090 kg

Initial velocity of bullet (u_{1}) =
1.5 m/s

Initial velocity of plank (u_{2}) =
0 m/s

**To find**: Common velocity (v) =?

Formula: m_{1 }u_{1} + m_{2}
u_{2 }= m_{1 }v_{1} + m_{2} v_{2}

**Solution**: Let v_{1} and v_{2} be the common velocities of the bullet and plank v_{1} = v_{2} = v m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}

(0.01 × 1.5) + (0.09 × 0) = (0.01 × v) + (0.09 × v)

0.015 + 0 = v (0.01 + 0.09)

0.015 = 0.1v

v = 0.015/ 0.1

v = 0.15 m/s

**Ans**: The plank moves with a velocity of 0.15 m/s.

**d) A person swims 100 m in the first 40 s, 80 m in the next 40 s and 45 m in the last 20 s. What is the average speed? (Ans: 2.25 m/s**_{2}**) **

**Given: **

Total distance (d) = 100 + 80 + 45 = 225 m

Total time taken (t) = 40 + 40 + 20 = 100 sec

**To find**: Average speed =?

Formula: Average speed = Total distance covered/ Total time taken

**Solution**: Average speed = Total distance covered /Total time taken

= 225/ 100

= 2.25 m/s

**Ans:** The person swims with an average speed of 2.25 m/s.

**Can you tell? **

**Q 1. In which of the following examples can you sense motion? How will you explain presence and absence of motion? **

1. The flight of a bird

2. A stationary train

3. Leaves flying through air

4. A stone lying on a hill.

**Ans. **We can sense motion in the examples

(1) the flight of a bird and (3) leaves flying through air.

A body is said to be in motion if it changes its position with respect to its surroundings and at rest otherwise.

**Think about it: **

**1. You are travelling in a bus. Is the person sitting next to you in motion? **

Ans. The person sitting next to me is not in motion with respect to me, but that person is in motion with respect to a person on the road.

**2. What do you take into consideration to decide if an object is moving or not? **

Ans. We should see whether the object changes its position with respect to its surroundings to decide if an object is moving or not.

**Let’s try this: **

**(1) Measure the distance between point A and B in different way as shown in figure 1.1 (a). ( refer the text book)**

**Ans**. Students should measure from the text book.

**2. Now measure the distance along the dotted line. Which distance is correct according to you and why?**

Ans. Students should measure from the text book.

The distance measured along the curved path, including the loop, from A and B is the correct distance as far as the distance covered by a particle moving from A and B along that path is concerned. The distance measured along the dotted line gives the magnitude of the displacement of the particle from A to B.

But, if the motion of a particle is not under consideration, i.e., we simply wish to know the separation between A and B, the distance measured along the dotted line from A to B would be the correct one.

**Think about it.**

A. Sheetal first went to her friend Sangeeta’s house on her way to school (see figure 1.1b). ( refer the text book)

B. Prashant went straight from home to school. Both are walking with the same speed. Who will take less time to reach the school and why?

In the above example, is there a difference between the actual distance and the distance travelled? What is it?

Ans. Prashant will take less time to reach the school. The distance travelled by Sheetal = 500m + 1200m = 1700m,

the distance travelled by Prashant = 1300m.

The difference = 1700m – 1300m = 400m. Prashant and Sheetal walk with the same speed and the distance travelled by Prashant is less than that travelled by Sheetal. Therefore, Prashant will take less time to reach the school.

**Use your brain power!**

1. Every morning, Swaralee walks round the edge of a circular field having a radius of 100 m. As shown in figure 1.2 (a), if she starts from the point A and takes one round, how much distance has she walked and what is her displacement? 2. If a car, starting from point P, goes to point Q (see figure 1.2 b) and then returns to point P, how much distance has it travelled and what is its displacement?

### Extra Questions

**Fill in Blanks:**

1. **Distance** is the length of the actual path travelled by an object in motion while going from one point to another.

2. **Displacement** is the minimum distance between the starting and finishing points.

3. The distance travelled in a particular direction by an object in unit time is called its **velocity.**

4. The displacement that occurs in unit time is called **velocity**.

5. The units of speed and velocity are the **same**.

6. In the SI system, the unit of speed and velocity is **m/s** while in the CGS system, it is **cm/s**.

7. Speed is related to **distance** while velocity is related to the **displacement.**

8. If the motion is along a **straight line**, the values of speed and velocity are the same, otherwise they can be different.

9. The first scientist to measure speed as the distance /time was **Galileo**.

10. The speed of sound in dry air is **343.2 **m/s while the speed of light is about **3 × 108** m/s.

11. The speed of revolution of the earth around the sun is about **29770** m/s.

12. If an object covers equal distances in equal time intervals, it is said to be moving with **uniform** speed.

13. If an object covers unequal distances in equal time intervals, it is said to be moving with **non-uniform** speed.

14. The rate of change of velocity is called **acceleration.**

15. If the velocity of an object changes during a certain time period, then it is said to have **accelerated** motion.

16. If the velocity changes by equal amounts in equal time intervals, the object is said to be in **uniform **acceleration.

17. If the velocity changes by unequal amounts in equal time intervals, the object is said to be **non-uniform** acceleration.

18. When the velocity of an object increases, the acceleration is **positive.**

19. When the velocity of an object decreases with time, it has** negative** acceleration.

20. Negative acceleration is also called **deceleration**.

21. If the velocity of the object does not change with time, it has **zero** acceleration.

22. An object in **uniform** motion covers equal distances in equal time intervals.

23. For all uniformly accelerated motions, the velocity-time graph is a **straight line**.

24. For **non-uniformly** accelerated motions, the velocity-time graph may have any shape depending on how the acceleration changes with time.

25. The **velocity** of an accelerated object changes with time.

26. Change in the velocity can be due to a change in **direction** or **magnitude** of the velocity or both.

27. When an object moves with constant speed along a circular path, the motion is called **uniform circular motion**.

28. An object continues to remain at rest or in a state of uniform motion along a straight line unless an external **unbalanced **force acts on it.

29. The effect of one object striking another object depends both on the mass of the former object and its **velocity**.

30. Momentum has **magnitude** as well as direction.

31. In SI system, the unit of momentum is **kg m/s**, while in CGS system, it is **g cm/s.**

32. If an unbalanced force applied on an object causes a change in the velocity of the object, then it also causes a change in its **momentum**.

33. The **force** necessary to cause a change in the momentum of an object depends upon the rate of change of momentum.

34. **Momentum** is the product of mass and velocity of an object.

35. Momentum is a **vector** quantity.

36. The rate of change of **momentum** is proportional to the applied force and the change of momentum occurs in the direction of the force.

37. If the same force is applied on different objects, the change in momentum is the **same**.

38. In SI system, the unit of force is **newton**.

39. The force necessary to cause an acceleration of 1 m/s2 in an object of mass 1 kg is called 1 **newton**.

40. In CGS system the unit of force is a **dyne.**

41. The force necessary to cause an acceleration of 1 cm/s2 in an object of mass 1 gm is called 1 **dyne**.

42. Force is a **reciprocal** action between two objects.

43. The forces between two objects are always equal and **opposite**.

44. Every action force has an equal and opposite reaction force which acts **simultaneously**.

45. Action and reaction forces act on different objects. They do not act on the same object and hence cannot **cancel** each other’s effect.

46. When no external force acts on two interacting objects, their total momentum remains **constant**.

47. When two objects collide, the total momentum before collision is **equal** to the total momentum after collision.

48. As the mass of the gun is much higher than the mass of the bullet, the velocity of the gun is much **smaller** than the velocity of the bullet.

49. The magnitude of the momentum of the bullet and that of the gun are equal and their directions are **opposite**.

50. Total momentum is also **constant** during the launch of a rocket.