Ch.1: Laws of Motion
- Arrowmite
- Mar 29
- 23 min read
Laws of Motion | Class 9 | Science | Chapter 1 | Maharashtra State Board
Explore the concept of motion through topics like distance and displacement, speed, velocity, acceleration, and Newton’s laws of motion. This chapter uses real-life examples and practical exercises to simplify complex scientific ideas.
Questions & Answers
1. Match the first column with appropriate entries in the second and third columns and remake the table.
S.No. | Column 1 | Column 2 | Column 3 |
1 | Negative acceleration | The velocity of the ob ject 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 acceleration | The velocity of the object increases | A vehicle moving with the velocity of 10 m/s, stops after 5 seconds. |
Ans.
S.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 acceleration | The velocity of the ob ject remains constant | A vehicle is moving with a velocity of 25 m/s |
2. Clarify the differences
A. Distance and displacement
Ans.
Distance | Displacement | |
1. | Distance is the length of the actual path travelled by an object. | Displacement is the minimum distance between the starting and finishing points. |
2. | It is a scalar quantity. | It is a vector quantity. |
3. | It is either equal to or greater than displacement. | It is either equal to or less than distance. |
4. | Distance travelled is always positive. | Displacement may be positive or negative or zero. |
B. Uniform and non-uniform motion.
Ans.
Uniform motion | Non-uniform motion | |
1. | If an object covers equal distances in equal intervals of time it is said to be in uniform motion. | If an object moves unequal distances in equal intervals of time, its motion is said to be nonuniform. |
2. | Distance – time graph for uniform motion is a straight line. | Distance – time graph for non-uniform motion is not a straight line. |
3. | In uniform motion, acceleration is zero. | In non-uniform motion acceleration is non-zero. |
3. Complete the following table.
Ans.
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.
Explanation:
Displacement is a vector quantity that measures the shortest straight-line distance between the starting and ending points of an object’s motion, along with its direction. Unlike distance, which measures the total path traveled, displacement only considers the initial and final positions.
b. Deceleration is negative acceleration.
Explanation:
Deceleration occurs when an object slows down, meaning its velocity decreases over time. It’s called negative acceleration because the rate of change of velocity is in the opposite direction to the motion of the object. For example, when a car applies brakes, it experiences deceleration.
c. When an object is in uniform circular motion, its direction changes at every point.
Explanation:
In uniform circular motion, the object moves along a circular path at a constant speed. However, since velocity depends on both speed and direction, and the direction of the object keeps changing at every point along the circle, the object’s velocity also changes constantly. This results in centripetal acceleration, directed toward the center of the circle.
d. During collision, momentum remains constant.
Explanation:
According to the law of conservation of momentum, the total momentum of a system of objects remains constant before and after a collision, provided no external force acts on it. This means the total momentum of the objects involved in a collision is the same both before and after the event.
e. The working of a rocket depends on Newton’s third law of motion.
Explanation:
Newton’s third law of motion states that “For every action, there is an equal and opposite reaction.” A rocket works by expelling gases backward at high speed (action), and as a result, the rocket moves forward (reaction). This principle explains how rockets propel themselves in space.
5. Give scientific reasons.
a. When an object falls freely to the ground, its acceleration is uniform.
Ans.
When the body falls freely to the ground, there are equal changes in velocity of the body in equal intervals of time.
Thus the acceleration of the body is constant, and it possesses uniform acceleration.
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.
Action and reaction forces act on different bodies.
They don’t act on the same body, hence they cannot cancel each other’s effect.
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 traveling with the same velocity.
Ans.
Momentum of an object depends on its mass as well as its velocity.
Cricket ball is heavier than a tennis ball. Although they are thrown with the same velocity, cricket ball has more momentum than a tennis ball.
The force required to stop a cricket ball is more than a tennis ball.
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.
When a body is at rest there is no change in velocity.
A body with constant velocity is said to be in uniform motion.
Hence, the state of 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. Kicking a football (Newton’s First Law – Law of Inertia)
Example: A football lying on the ground stays at rest until you kick it. Once kicked, it keeps moving until friction from the ground and air resistance slows it down and eventually stops it.
Explanation: This illustrates Newton’s First Law, which states that an object remains at rest or in uniform motion unless acted upon by an external force. Here, the force of your kick sets the ball in motion, and friction brings it to a stop.
2. Riding a bicycle (Newton’s Second Law – F = ma)
Example: When you pedal a bicycle harder, it speeds up; when you reduce the force, it slows down. The heavier the load on the bicycle, the harder you have to pedal to accelerate.
Explanation: This follows Newton’s Second Law, which states that the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass (F = ma). More force on the pedals = greater acceleration; more weight = slower acceleration.
3. Jumping off a small boat onto the shore (Newton’s Third Law – Action and Reaction)
Example: When you jump off a boat toward the shore, the boat moves backward in the opposite direction.
Explanation: This demonstrates Newton’s Third Law, which states that “For every action, there is an equal and opposite reaction.” Your jump pushes the boat backward while propelling you forward toward the shore.
4. Car suddenly stopping and passengers lurching forward (Newton’s First Law – Law of Inertia)
Example: When a moving car comes to a sudden stop, the passengers jerk forward.
Explanation: This happens because of inertia — the tendency of objects to resist changes in motion. When the car stops, your body wants to keep moving forward at the same speed until the seatbelt or dashboard applies a force to stop you.
5. A rocket launch (Newton’s Third Law – Action and Reaction)
Example: A rocket launches into the sky by expelling gases downward at high speed.
Explanation: The downward force of the expelled gases (action) creates an equal and opposite upward force (reaction) that lifts the rocket into the air, perfectly showing Newton’s Third Law.
7. Solved 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? (Ans: 6 m/s)
Ans.
Given:
Distance traveled in the first 3 seconds = 18 m
Distance traveled in the next 3 seconds = 22 m
Distance traveled in the last 3 seconds = 14 m
Total time = 3 s + 3 s + 3 s = 9 s
Total distance traveled:
Total Distance = 18+22+14 = 54 m
Average speed formula:
Average Speed = Total Distance / Total Time
Substitute the values:
Average Speed = 54 / 9 = 6 m/s
Final Answer: 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? (Ans: 48 N, 2 m/s2)
Ans.
Given:
Mass of the object (m) = 16 kg
Acceleration (a) = 3 m/s²
We use Newton’s Second Law of Motion:
F = m × a
Substitute the values:
F = 16 × 3 = 48 N
So the applied force is 48 N. ✅
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 900 g. The plank was initially at rest. The bullet gets embedded in the plank and both move together. Determine their velocity. (Ans: 0.15 m/s)
Ans.
Given:
Mass of the bullet (m1) = 10 g = 0.01 kg
Velocity of the bullet (v1) = 1.5 m/s
Mass of the wooden plank (m2) = 900 g = 0.9 kg
Velocity of the plank (v2) = 0 m/s (initially at rest)
After the bullet gets embedded in the plank, both move together with the same velocity (v).
Using the law of conservation of momentum:
Total momentum before collision = Total momentum after collision
m1v1+m2v2 = (m1+m2)v
Substitute the values:
(0.01)(1.5)+(0.9)(0) = (0.01+0.9)v
Simplify:
0.015=(0.91)v
Solving for v:
v=0.015 / 0.91 = 0.01648 ≈ 0.015 m/s
Final Answer: v = 0.015 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/s2)
Ans.
Given:
Distance covered in the first 40 s = 100 m
Distance covered in the next 40 s = 80 m
Distance covered in the last 20 s = 45 m
Total distance traveled:
Total Distance = 100+80+45=225 m
Total time taken:
Total Time = 40+40+20 = 100 s
Formula for average speed:
Average Speed = Total Distance / Total Time
Substitute the values:
Average Speed = 225/100 = 2.25 m/s
Final Answer: 2.25 m/s ✅
E X T R A
1. Choose and write the correct option:
1. The displacement that occurs in unit time is called …………….. .
(a) displacement
(b) distance
(c) velocity
(d) acceleration
Ans.
(c) velocity
2. The unit of velocity in the SI system is …………….. .
(a) cm/s
(b) m/s2
(c) um/s2
(d) m/s
Ans.
(d) m/s
3. v2 = u2 + 2as is the relation between and …………….. .
(a) speed and velocity
(b) distance and acceleration
(c) displacement and velocity
(d) speed and distance
Ans.
(c) displacement and velocity
4. …………….. is the relation between displacement and time.
(a) v = u + at
(b) v2 = u2 + 2as
(c) s = ut + 1/2 at2
(d) v = u + 2as
Ans.
(c) s = ut + 1/2 at2
5. The force necessary to cause an acceleration of 1 m/s2 in an object of mass 1 kg is called …………….. .
(a) 1 dyne
(b) 1 m/s
(c) 1 Newton
(d) 1 cm/s
Ans.
(c) 1 Newton.
6. Even if the displacement of an object is zero, the actual distance traversed by it …………….. .
(a) may not be zero.
(b) will be zero
(c) will be constant
(d) will be infinity
Ans.
(a) may not be zero
7. If the velocity changes by equal amounts in equal time intervals, the object is said to be in …………….. .
(a) uniform acceleration
(b) uniform velocity
(c) non-uniform acceleration
(d) non-uniform motion
Ans.
(a) uniform acceleration
8. If an object is moving with a uniform velocity …………….. .
(a) its speed remains the same, but direction of motion changes
(b) its speed changes but direction of motion is same
(c) its speed and direction both change
(d) its speed and direction both remain the same
Ans.
(d) its speed and direction both remain the same
9. is an example of positive acceleration.
(a) A stone is thrown vertically upwards
(b) A stone falls freely towards the earth
(c) Brakes are applied by the truck driver
(d) The train arriving at the station
Ans.
(b) a stone falls freely towards the earth
10. An object continues to remain at rest or in a state of uniform motion along a straight line unless an …………….. acts on it.
(a) internal imbalanced force
(b) external unbalanced force
(c) internal balanced force
(d) external balanced force
Ans.
(b) external unbalanced force
11. The …………….. is proportional to the applied force and it occurs in the direction of the force.
(a) change of momentum
(b) rate of change of velocity
(c) change of velocity
(d) rate of change of momentum
Ans.
(d) rate of change of momentum
12. …………….. is a relative concept.
(a) Motion
(b) Direction
(c) Power
(d) Acceleration
Ans.
(a) Motion
13. A body is said to be in motion if it changes its …………….. with respect to its surroundings.
(a) position
(b) direction
(c) speed
(d) force
Ans.
(a) position
14. A body is said to be at …………….. if it does not change its position with respect to its surroundings.
(a) Motion
(b) Rest
(c) Gravity
(d) Force
Ans.
(b) Rest
15. …………….. is the length of the actual path travelled by an object in motion while going from one point to another.
(a) Distance
(b) Displacement
(c) Speed
(d) Velocity
Ans.
(a) Distance
16. The distance covered by a body in unit time is called its …………….. .
(a) velocity
(b) speed
(c) displacement
(d) rest
Ans.
(b) speed
17. S.I. unit of speed is …………….. and in C.G.S unit it is …………….. .
(a) m/s and cm/s
(b) km/s and cm/s
(c) m/s and mm/s
(d) m/s and nm/s
Ans.
(a) m/s , cm/s
18. The distance travelled in a particular direction by an object in unit time is called its …………….. .
(a) velocity
(b) speed
(c) displacement
(d) rest
Ans.
(a) velocity
19. Units of speed and velocity are the
(a) Same
(b) Different
(c) Greater than each other
(d) Unequal
Ans.
(a) same
20. …………….. . is related to distance, while …………….. is related to displacement.
(a) Gravity and magnetism
(b) Speed and force
(c) Speed and velocity
(d) Motion and rest
Ans.
(c) Speed, velocity
21. If an object covers equal distances in equal time intervals, it is said to be moving with …………….. speed.
(a) Uniform
(b) Non uniform
(c) Changing
(d) Random
Ans.
(a) uniform
22. If an object covers unequal distances in equal time Intervals, it is said to be moving with speed.
(a) Uniform
(b) Non uniform
(c) Changing
(d) Random
Ans.
(b) non uniform
23. The rate of change of velocity is called
(a) Speed
(b) Acceleration
(c) Velocity
(d) Rest
Ans.
(b) acceleration
24. Speed of light in dry air is …………….. m/s.
(a) 3 x 10^7
(b) 3 x 10^8
(c) 3 x 10^9
(d) 3 x 10^3
Ans.
(b) 3 x 10^8
25. When velocity of a body increases, its acceleration is …………….. .
(a) Negative
(b) Zero
(c) Positive
(d) Equal
Ans.
(c) positive
26. When velocity of a body decreases, its acceleration is …………….. .
(a) Negative
(b) Zero
(c) Positive
(d) Equal
Ans.
(a) negative
27. Negative acceleration is also called or
(a) Deceleration or retardation
(b) Deceleration or acceleration
(c) acceleration or retardation
(d) Zero
Ans.
(a) deceleration or retardation
28. In case of motion, object travels equal …………….. in equal intervals of time.
(a) Uniform, distance
(b) Non-Uniform, distance
(c) Uniform, displacement
(d) Uniform, displacement
Ans.
(a) uniform, distances
29. Motion of an object was studied by …………….. .
(a) Sir Albert Einstein
(b) Sir Thomas Edison
(c) Sir Isaac Newton
(d) Sir Ravindranath Tagore
Ans.
(c) Sir Issac Newton
30. When an object moves in a circular path with uniform speed, its motion is ………….. motion.
(a) Non uniform circular
(b) Random circular
(c) Uniform circular
(d) Uniform linear
Ans.
(c) uniform circular
31. When a coin moves along a circular path, the direction of its motion at every point is …………….. .
(a) Circular
(b) Concave
(c) Tangential
(d) Convex
Ans.
(c) tangential
32. For all uniformly accelerated motions, the velocity-time graph is a …………….. .
(a) Curved line
(b) Straight line
(c) Negative line
(d) Positive line
Ans.
(b) straight line
33. In the distance-time graph, the slope of the straight line indicates …………….. .
(a) Acceleration
(b) Velocity
(c) Speed
(d) Rest
Ans.
(b) velocity
34. The first equation of motion gives relation between …………….. and time.
(a) Acceleration
(b) Velocity
(c) Speed
(d) Rest
Ans.
(b) velocity
35. Newton’s first law explains the phenomenon of
(a) Rest
(b) Inertia
(c) Speed
(d) Velocity
Ans.
(b) inertia
36. …………….. cause a change in the state of an object at rest or in uniform motion.
(a) Balanced forces
(b) Zero forces
(c) Unbalanced forces
(d) None of them
Ans.
(c) Unbalanced forces
37. To describe an object’s momentum, we must specify its …………….. and …………….. .
(a) Mass and displacement
(b) Mass and direction
(c) Mass and velocity
(d) Mass and acceleration
Ans.
(c) mass and velocity
38. …………….. is the product of mass and velocity of an object.
(a) Speed
(b) Acceleration
(c) Momentum
(d) Force
Ans.v
(c) Momentum
39. The rate of change of momentum is proportional to the applied …………….. .
(a) Balanced force
(b) Unbalanced force
(c) Mass
(d) Velocity
Ans.
(b) unbalanced force
40. S.I. unit of momentum is
(a) kg cm/s
(b) kg m/s
(c) gm/s
(d) m/s
Ans.
(b) kg m/s
41. …………….. is always conserved in a collision.
(a) Force
(b) Power
(c) Speed
(d) Total momentum
Ans.
(d) Total momentum
42. When a bullet is fired from the gun, the gun moves in backward direction. This motion is called as …………….. .
(a) Momentum
(b) Velocity
(c) Acceleration
(d) Recoil
Ans.
(d) Recoil
43. In CGS system, the unit of force is …………….. .
(а) Newton
(b) Watt
(c) Horse power
(d) Dyne
Ans.
(d) Dyne.
2. Find the odd man out:
1. Displacement, Force, Momentum, Mass
Ans.
Mass
2. Speed, Power, Energy, Acceleration
Ans.
Acceleration
3. Newton’s 1st law, Newton’s 2nd law, Newton’s 3rd law, Kepler’s laws of motion
Ans.
Newton’s 3rd law
3. Find out the correlation
1. Speed zero: Body at rest :: Negative acceleration : Retardation
Ans.
Retardation
2. Displacement : Vector quantity :: Distance : Scalar quantity
Ans.
Vector quantity
3. When body comes to rest at the end of the motion : Final velocity is zero :: When body is at rest at the starting of motion : Initial velocity is zero
Ans.
Initial velocity is zero
4. Uniform circular motion: Displacement is zero :: Uniform velocity : Acceleration is zero
Ans.
Displacement is zero
5. Inertia : Newton’s 1st law :: Rate of change of momentum : Newton’s 2nd law
Ans.
Newton’s 2nd law
6. Balanced force : Body at rest :: Force equation : Mass x acceleration
Ans.
Body at rest
4. Distinguish between:
1. Positive acceleration and Negative acceleration
Ans.
Positive acceleration | Negative acceleration | |
1. | When the velocity of a body increases, acceleration is said to be positive acceleration. | When the velocity of a body decreases, acceleration is said to be negative acceleration. |
2. Scalar quantity and Vector quantity
Ans.
Scalar quantity | Vector quantity | |
1. | Scalar quantities are physical quantities having magnitude only. | Vector quantities are physical quantities having both magnitude and direction. |
3. Balanced force and Unbalanced force
Ans.
Balanced force | Unbalanced force | |
1. | Balanced force keeps the body at rest. | Balanced force keeps the body at rest. |
5. State whether the following statements are true or false:
1. The velocity of a body is given by the distance covered by it in unit time in a given direction.
Ans.
True
2. Displacement is a scalar quantity
Ans.
False
3. Uniform acceleration means that the body is moving with a uniform velocity.
Ans.
False
4. The direction of acceleration can be opposite to that of velocity.
Ans.
True
5. Work is a vector quantity.
Ans.
False
6. Displacement is always greater than distance.
Ans.
False
7. The distance and displacement are equal only if, motion is along a straight path.
Ans.
True
8. If an object experiences acceleration, a force is acting on it.
Ans.
True
9. A train pulling out from a station is in uniform motion.
Ans.
False
10. If a bus in motion is suddenly stopped, the passengers fall backwards.
Ans.
False
11. If a single force is acting on an object, it will always accelerate.
Ans.
True
12. In circular motion, direction of motion is tangential.
Ans.
True
13. The inertia of a body is measured in terms of its mass.
Ans.
True
6. Name the following:
1. The scientist who summarized motion in a set of equations of motion.
Ans.
Isaac Newton
2. Motion of an object along a circular path with uniform speed.
Ans.
Uniform circular motion
3. What is the backward motion of the gun called?
Ans.
Recoil
4. The motion in which the object covers equal distance in equal intervals of time.
Ans.
Uniform motion
5. S. I. unit of acceleration.
Ans.
m/s2
6. CGS unit of momentum.
Ans.
g cm/s
7. Answer the following in one sentence:
1. When is acceleration said to be positive?
Ans.
When the velocity of a body increases, acceleration is said to be positive acceleration.
2. What is negative acceleration?
Ans.
When the velocity of a body decreases, acceleration is said to be negative acceleration.
3. What is the direction of velocity of an object performing uniform circular motion?
Ans.
The direction of velocity is along the tangential direction to its position.
4. What kind of force keeps the body at rest?
Ans.
Balanced force keeps the body at rest.
5. Which law of motion gives the measure of force?
Ans.
Newton’s second law of motion gives the measure of force.
6. What are vectors and scalars?
Ans.
Scalars are physical quantities having magnitude only whereas, vectors are physical quantities having both magnitude and direction.
7. Which of the quantities distance, speed, velocity, time and displacement are scalars and which are vectors?
Ans.
Distance, speed and time are scalars displacement and velocity are vectors.
8. Give scientific reasons:
1. Motion is relative.
Ans.
The motion of an object depends on the observer, hence a body may appear moving for one person and at the same time at rest for another one.
Hence, motion is relative.
2. Newton’s first law of motion is called as law of inertia.OR Heavier objects offer more inertia.
Ans.
Inertia is related to the mass of the object.
As mass is the quantity of matter in a body, we need to exert more force to push a heavier body.
Hence heavier objects offer more inertia.
As the same property is described by Newton’s first law of motion, it is called as Law of Inertia.
3. The launching of a rocket is based on Newton’s third law of motion.
Ans.
Newton’s third law of motion states that ‘Every action force has an equal and opposite reaction force which acts simultaneously.’
When the fuel in a rocket is ignited, it bums as a result of chemical reaction.
The exhaust gases escape with a great force in the backward direction.
It exerts an equal and opposite reaction force on the rocket, due to which the rocket moves in the forward direction.
Thus, the principle of launching of rocket is based on Newton’s third law of motion.
9. Answer the following in short:
1. Explain the three different ways to change the velocity.
Ans.
As velocity is related to speed and direction, it can be changed by :
Changing the speed while keeping the direction constant.
Changing direction while keeping speed constant.
Changing both speed as well as direction of motion.
2. Explain what is positive, negative and zero acceleration.
Ans.
Positive Acceleration: When the velocity of an object increases, the acceleration is positive. In this case, the acceleration is in the direction of velocity.
Negative Acceleration: When the velocity of an object decreases with time, it has negative acceleration. Negative acceleration is also called deceleration. Its direction is opposite to the direction of velocity.
Zero Acceleration: If the velocity of the object does not change with time, it has zero acceleration.
3. What inference do we draw from the velocity-time graph for a uniformly accelerated motion?
Ans.
From velocity-time graph we can infer whether velocity changes by equal amounts in equal intervals of time or not.
Thus, for all uniformly accelerated motion, the velocity – time graph is a straight line and slope of the line gives the acceleration.
For non-uniformly accelerated motion, velocity-time graph can have any shape according to variation in velocity with respect to time.
4. State the three equations of motion and give the relationship explained by them.
Ans.
v = u + at: This is the relation between velocity and time.
s = ut + 1/2 at2 : This is the relation between displacement and time
v2 = u2 + 2as : This is the relation between displacement and velocity.
5. What are the implications of Newton’s Third Law of motion?
Ans.
Action and reaction are terms that express force.
These forces act in pairs. One force cannot exist by itself.
Action and reaction forces act simultaneously.
Action and reaction forces act on different objects. They do not act on the same object and hence cannot cancel each other’s effect.
6. Explain recoil and recoil velocity. Derive its expression.
Ans.
Let us consider the example of a bullet fired from a gun. When a bullet of mass nij is fired from a gun of mass m2, its velocity becomes v2, and its momentum becomes m^. Before firing the bullet, both the gun and the bullet are at rest. Hence, total initial momentum is zero.
According to Newton’s third law of motion, the total final momentum also has to be zero. Thus, the forward-moving bullet causes the gun to move backward after firing.
This backward motion of the gun is called its recoil. The velocity of recoil, v2 is such that,
m1v1+m2v2=0 or v2 = -m1/m2 × v1
10. Distinguish between:
1. Speed and velocity.
Ans.
Speed | Velocity | |
1. | Speed is the distance covered by a body in unit time. | The displacement that occurs in unit time is called velocity. |
2. | It is a scalar quantity. | It is a vector quantity. |
3. | Speed is equal to or greater than velocity. | Velocity is equal to or less than speed. |
4. | Speed = distance/time | Velocity = displacement/time |
5. | It is always positive or zero but never negative. | It may be positive, Zero or negative. |
2. Balanced force and unbalanced force.
Ans.
Balanced force | Unbalanced force | |
1. | Two equal forces applied on a body in the opposite direction. | Two unequal forces applied on a body. |
2. | This force does not change the state of rest or the state of uniform motion. | This force can change the state of rest or the state of uniform motion of a body in a straight line. |
11. Write laws and explain write implications:
1. Newton’s third law of motion
Ans.
‘Every action force has an equal and opposite reaction force which acts simultaneously’.
Action and reaction are terms that express force.
These forces act in pairs. One force cannot exist by itself.
Action and reaction forces act simultaneously.
Action and reaction forces act on different objects. They do not act on the same object and hence cannot cancel each other’s effect.
2. Explain Newton’s second law of motion and derive the formula.
Ans.
Newton’s second law explains about change in momentum. It states that The rate of change of momentum is proportional to the applied force and the change of momentum occurs in the direction of the force.
Suppose an object of mass ‘m’ has an initial velocity ‘u. When a force ‘F’ is applied in direction of its velocity for time ‘t’, its velocity becomes ‘y’. Then, the total initial momentum of the body = ‘mu’. Its final momentum after time t = ‘mv’.
So, the rate of change of momentum
= Change in momentum / time
= mv - mu / t
= m(v-u) / t
= ma ..... ∴ a = (v-u) / t
Hence by Newtons second law of motion, for the rate of change of momentum is proportional to the applied force.
∴ ma ∝ F
∴ F ∝ ma
∴ F ∝ kma (k = Constant of proportionaLity and value is 1).
∴ F = ma
3. State the law of conservation of momentum and derive the formula.
Ans.
Let mass of object A and B be m1 and m1 respectively.
Let their initial velocity be u1 and u2 Let their final velocity be v1 and v2
We know,
P = mv
Let their initial momentum be m1u1 and m2 u2
Let their final momentum be m1v1 and m2v2
Total initial momentum = (m1u1 + m2u2)
Total final momentum = (m1v1 + m2v2)
If F2 is the force that acts on object B,
F2 = -F1
m2a2 = -m1a1 .......... [∴ f=ma]
m2 × (v2-u2)/t = m1 × (v1-u1)/t ............. [∴a = (v-u)/t]
∴ m2 (v2-u2) - m1 (v1-u1)
∴ m2v2 - m2u2 = -m1v1 + m1u1
∴ (m2v2 + m1v1) = m2u2 + m1u1
i.e. The magnitude of total of total final momentum = the magnitude of total initial momentum.
12. Complete the paragraph:
1. Moving Objects
Ans.
‘Distance’ is the length of the actual path travelled by an object in motion while going from one point to another, whereas displacement is the minimum distance between the starting and finishing points. The displacement that occurs in unit time is called velocity. The units of speed and velocity are the same. In the SI system, the unit is m/s while in the CGS system; it is cm/s. Speed is related to distance while velocity is related to the displacement. If the motion is along a straight line, the values of speed and velocity are the same, otherwise they can be different. The first scientist to measure speed as the distance /time was Galileo. The speed of sound in dry air is 343.2 m/s while the speed of light is about 3 x 108 m/s. The speed of revolution of the earth around the sun is about 29770 m/s.
2. Types of motion
Ans.
If an object covers unequal distances in equal time intervals, it is said to be moving with non-uniform speed. For example the motion of a vehicle being driven through heavy traffic. If an object covers equal distances in equal time intervals, it is said to be moving with uniform speed. The rate of change of velocity is called acceleration. If the velocity changes by equal amounts in equal time intervals, the object is said to be in uniform acceleration. If the velocity changes by unequal amounts in equal time intervals, the object are said to be non-uniform acceleration. The speed of the tip is constant, but the direction of its displacement and therefore, its velocity is constantly changing. As the tip is moving along a circular path, its motion is called uniform circular motion.
3. Newton’s laws and conservation of momentum
Ans.
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. The rate of change of momentum is proportional to the applied force and the change of momentum occurs in the direction of the force. Momentum has magnitude as well as direction. Its direction is the same as that of velocity. In SI system, the unit of momentum is kg m/s, while in CGS system, it is g cm/s. 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.
The force necessary to cause a change in the momentum of an object depends upon the rate of change of momentum. Every action force has an equal and opposite reaction force which acts simultaneously. 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. The magnitude of the momentum of the bullet and that of the gun are equal and their directions are opposite. Thus, the total momentum is constant. Total momentum is also constant during the launch of a rocket.
13. Answer the following in detail:
1. What is speed? State its units and types. Explain instantaneous speed and average speed.
Ans.
The speed of a body is the distance travelled in unit time. The units of speed in CGS system is cm/s and in SI system is m/s.There are two types of speed :
Uniform speed : When a body covers equal distance in equal intervals of time throughout its motion, it is said to have uniform speed.
Non-uniform or variable speed: When a body covers unequal distance in equal intervals of time it is said to have non-uniform speed.
The speed of the body at any instant is called instantaneous speed. Average speed is the ratio of total distance covered to total time taken.
2. What is velocity? State its units and types.
Ans.
The velocity of a body is the distance travelled by a body in a particular direction in unit time. Thus, rate of change of displacement is called velocity.
v = s/t
where: s = displacement; t = time taken; v = velocity
3. What is acceleration? State its units and types.
Ans.
(i) Acceleration is a rate of change in velocity. It is a vector quantity, a=v−u/t
where : v = final velocity; u = initial velocity;
a = acceleration
Units of acceleration in SI system is m/s2 and CGS system is cm/s2.
(ii) Types of acceleration:
(a) Uniform acceleration : If the change in velocity is equal in equal intervals of time, the acceleration is uniform acceleration.
(b) Non-uniform acceleration : If the change in velocity is unequal in equal intervals of time, the acceleration is a non-uniform acceleration.
(iii) Kinds of acceleration:
Positive acceleration : When the velocity of an object goes on increasing, it is said to have Positive acceleration.
Negative acceleration : When the velocity of an object goes on decreasing, it is said to have negative acceleration or retardation or deceleration.
Zero acceleration : If the velocity of the object does not change with time, it has zero acceleration.
4. Explain Newton’s second law of motion and derive the formula.
Ans.
Newton’s second law explains about change in momentum. It states that ‘The rate of change of momentum is proportional to the applied force and the change of momentum occurs in the direction of the force.’
Suppose an object of mass’m’ has an initial velocity ‘u’. When a force ‘F’ is applied in the direction of its velocity for time’t’, its velocity becomes ‘v’. Then, the total initial momentum of the body = ‘mu’. Its final momentum after time t = ‘mv’.
So, the rate of change of momentum
= Change in momentum / time
= mv - mu / t
= m(v-u) / t
= ma ..... ∴ a = (v-u) / t
Hence by Newtons second law of motion, for the rate of change of momentum is proportional to the applied force.
∴ ma ∝ F
∴ F ∝ ma
∴ F ∝ kma (k = Constant of proportionaLity and value is 1).
∴ F = ma
5. State the law of conservation of momentum and derive the formula.
Ans.
(i) Let mass of objects A and B be and m2 respectively
Let their initial velocity be m1 and u2
Let their final velocity be V1 and v2
(ii) We know,
P = mv
Let their initial momentum be m1u1 and m2u2
Let their final momentum be m1v1 and m2v2
(iii) Total initial momentum = (m1u1 + m2u2)
Total final momentum = (m1v1 + m2v2)
(iv) If F2 is the force that acts on object B,
F2 = -F1
m2a2 = -m1a1 .......... [∴ f=ma]
m2 × (v2-u2)/t = m1 × (v1-u1)/t ............. [∴a = (v-u)/t]
∴ m2 (v2-u2) - m1 (v1-u1)
∴ m2v2 - m2u2 = -m1v1 + m1u1
∴ (m2v2 + m1v1) = m2u2 + m1u1
i.e. The magnitude of total of total final momentum = the magnitude of total initial momentum.
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