Chapter 2 – Force and Motion | Chapter Solution Class 9

Distance is the total length of the path traveled by a moving object in a given time. It is a scalar quantity and has only magnitude but no direction.

Displacement is the shortest straight-line distance between the initial and final positions of a moving object, along with its direction. It is a vector quantity.

A body is said to be in uniform motion when it covers equal distances in equal intervals of time in a straight line.

The motion of a car moving through traffic, where its speed changes at different intervals, is an example of non-uniform motion.

Speed is the rate at which an object covers distance.

The SI unit of speed is meter per second (m/s).

The path of a body in uniform motion is a straight line.

Velocity is the rate of change of displacement of a body in a particular direction. It is a vector quantity.

Velocity is a vector quantity as it has both magnitude and direction.

A car slowing down as it approaches a traffic signal is an example of retardation (negative acceleration).

The slope of a velocity-time graph represents acceleration.

Force is that which, when applied to a body, changes or tends to change its state of rest or uniform motion in a straight line.

When two or more forces acting on a body do not cancel each other, resulting in a net force that changes the motion of the body, they are called unbalanced forces.

Newton’s first law states that a body remains in its state of rest or uniform motion unless acted upon by an unbalanced external force.

Inertia is the tendency of an object to resist changes in its state of motion or rest.

Momentum of a body depends on its mass and velocity.

Momentum is the product of an object’s mass and velocity. It is given by momentum (p) = mass (m) × velocity (v).

Newton’s third law states that for every action, there is an equal and opposite reaction.

The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external force acts on it.

The product of mass and velocity of a body is called momentum.

A rocket works on the principle of conservation of linear momentum.

Change in velocity in time interval t ⇒ BE = BD – ED

If AE be drawn parallel to OD, then from the graph,

BD = BE + ED = BD + OA

or, v = BE + u

or, BE = v – u

Now, acceleration, a = \text{Change in velocity}\over \text{time}

= BE\over AE

= \text{BE}\over \text{OD}

Putting OD = t  ⇒ a = \text{BE}\over \text{t}

⇒  BE = at = v – u

therefore, v = u + at

A newton (N) is the force that produces an acceleration of 1 m/s² when applied to a mass of 1 kg.

In CGS, the absolute unit of force is dyne, where 1 N = 10⁵ dyne.

Yes, it is possible. For example, when a person completes a round in a circular track and returns to the starting point, the total distance covered is nonzero, but displacement is zero since the initial and final positions are the same.

Forces are balanced when equal and opposite forces act on a body, keeping it in equilibrium. Example: A book resting on a table. Balanced forces do not cause motion but can change the shape of an object, like pressing a rubber ball.

The changes that a force can bring about on a body are:

• Change the state of motion (e.g., a football starts moving when kicked).
• Change the speed (e.g., applying brakes in a car).
• Change the direction (e.g., a bat hitting a ball).
• Change the shape (e.g., squeezing a sponge).

Due to inertia of motion, the body remains in motion even after jumping. If the person suddenly stops on landing, they may fall forward and get injured. To avoid this, a person should run in the direction of the bus after jumping.

According to Newton’s First Law, an object in motion remains in motion unless acted upon by an external force. No force is required to maintain uniform velocity in an ideal case without friction, as there is no opposing force.

By lowering the hands, the player increases the time of impact, reducing the rate of change of momentum. This decreases the force exerted on the hands, preventing injury. This is based on the impulse-momentum principle.

Action and reaction forces act on different objects, not on the same object. Since they act on different bodies, they do not cancel out but instead result in changes in motion as per Newton’s Third Law.

First distance traveled = 16 m

Time taken for first distance = 4 s

Second distance traveled = 16 m

Time taken for second distance = 2 s

Total distance traveled = 16 + 16 = 32 m

Total time taken = 4 + 2 = 6 s

Average speed = \text{total distance traveled} \over \text{total time taken}

Average speed = 32 \over 6 = 5.33 m/s

Answer: The average speed of the object is 5.33 m/s.

Length of the pool = 90 m

Total distance covered = 180 m

Total time taken = 1 minute = 60 seconds

Average speed = \text{total distance traveled} \over \text{total time taken}

= 180 \over 60

= 3 m/s

Displacement = shortest distance between initial and final position

Since the girl returns to the starting point, displacement = 0 m

Average velocity = \text{displacement} \over \text{total time taken}

Average velocity = 0 \over 60 = 0 m/s

Initial velocity (u) = 18 km/h = 18 × {5\over 18} = 5 m/s

Final velocity (v) = 36 km/h = 36 × {5\over 18} = 10 m/s

Time, t = 5 s

(i) Acceleration (a) = \text{v - u} \over \text{t}

a = 10 - 5 \over 5

a = 5 ÷ 5

a = 1 m/s²

(ii) Distance covered (s) is given by the equation:

s = ut + (1 ÷ 2) × a × t²

s = (5 × 5) + (1 ÷ 2) × 1 × (5 × 5)

s = 25 + (1 ÷ 2) × 25

s = 25 + 12.5

s = 37.5 m

Diameter of circular track = 200 m

Radius (r) = 200 ÷ 2 = 100 m

Circumference of track = 2 × π × r

= 2 × 3.14 × 100

= 628 m

Time taken for one round = 40 s

Total time given = 2 min 20 s = 140 s

Number of rounds completed = 140 ÷ 40

= 3.5 rounds

(i) Distance covered = Number of rounds × Circumference

Distance = 3.5 × 628 = 2198 m ≈ 2200 m

(ii) Displacement:

After 3 rounds, the athlete returns to the starting point, so displacement = 0.

For the extra 0.5 round, the athlete reaches the opposite point of the circle.

The displacement is the diameter of the circle = 200 m.

Length of the road around the garden = 600 m

Since the man completes one full round and returns to the starting point, the initial and final positions are the same.

Displacement is the shortest distance between the initial and final positions.

Since the initial and final positions coincide, the displacement is 0 m.

Initial velocity, u = 30 km/h

Final velocity, v = 60 km/h

Time, t = 1 min = 1/60 hour

Acceleration (a) = \text{v - u} \over \text{t}

a = 60 - 30 \over {1\over 60}

a = 30 × 60

a = 1800 km/hr²

Thus, the acceleration of the train is 1800 km/hr².

Force, F = 50 dyne

Mass, m = 10 g

Acceleration (a) = Force / Mass

a = 50 / 10

a = 5 cm/s²

The acceleration produced by the force is 5 cm/s².

Mass, m = 10 g

Acceleration, a = 5 cm/s²

Force (F) = Mass × Acceleration

F = 10 × 5

F = 50 dyne

The force acting on the mass is 50 dyne.

Mass, m = 250 g = 0.25 kg

Force, F = 1 newton

Acceleration (a) = Force / Mass

a = 1 / 0.25

a = 4 m/s²

Converting to cm/s²:

1 m/s² = 100 cm/s²

a = 4 × 100

a = 400 cm/s²

The acceleration of the body is 400 cm/s².

Initial velocity, u = 45 km/h

Acceleration, a = 20 cm/s² = 0.2 m/s²

Time, t = 25 s

u = (45 × 1000) ÷ (60 × 60) = 12.5 m/s

v = u + at

v = 12.5 + (0.2 × 25)

v = 12.5 + 5

v = 17.5 m/s

The velocity after 25 seconds is 17.5 m/s.

Mass, m = 10 g

Initial velocity (u) = 0 m/s

Final velocity (v) = 15 m/s

Time (t) = 5 s

Step 1: Calculate Acceleration

Acceleration (a) = \text{v - u} \over \text{t}

a = \text{15 - 0} \over \text{5}

a = 3 m/s²

Convert to cm/s²:

a = 3 × 100

a = 300 cm/s²

Step 2: Calculate Final Momentum

Momentum (p) = Mass × Velocity

p = 10 × 15

p = 150 g·cm/s

Step 3: Calculate Force

Force (F) = Mass × Acceleration

F = 10 × 3

F = 30 dyne

Answer:

• Acceleration = 3 cm/s²
• Final momentum = 150 g·cm/s
• Force = 30 dyne

Mass, m = 0.5 kg

Acceleration, a = 10 m/s²

Force (F) = Mass × Acceleration

F = 0.5 × 10

F = 5 N

The force applied on the body is 5 N.

(i) initial

(ii) graph

(iii) distance

(iv) acceleration

(v) speed

(vi) force

(vii) rest

(viii) newton

(ix) acceleration

(x) different bodies

True

Explanation: Motion is relative, meaning that if object A appears to move relative to object B, then object B also appears to move relative to object A but in the opposite direction.

True

Explanation: When a body moves in a straight line without changing direction, the displacement is equal to the total distance covered. However, if the path is curved, displacement is usually less than distance.

False

Explanation: According to Newton’s Third Law, action and reaction forces act on different objects, not the same object. For example, when a person pushes a wall, the wall pushes back on the person with an equal and opposite force.

True

Explanation: The inertia of a body depends on its mass. A heavier body has more inertia and resists changes in motion more than a lighter body, making it harder to start moving.

False

Explanation: When a passenger jumps from a moving bus, their body is in motion due to inertia. Since the feet stop upon landing, the upper body continues moving forward, causing the passenger to lean forward, not backward.

(b) moving with uniform speed

Explanation: When a body moves equal distances in equal intervals of time, its speed remains constant. If direction is not specified, it is called uniform speed. However, if the direction remains unchanged, it would be uniform velocity.

(a) a straight line

Explanation: The distance-time graph for uniform motion is a straight line with a constant slope, indicating a constant speed. A curved graph represents acceleration, and a horizontal line indicates rest.

(c) distance

Explanation: The area under a speed-time graph represents the total distance traveled by an object. This is because distance = speed × time, which corresponds to the area under the graph.

(a) velocity

Explanation: The slope of a distance-time graph gives the rate of change of distance with respect to time, which is velocity. If the graph is a straight line, the velocity is constant.

(a) Newton’s first law

Explanation: According to Newton’s First Law (Law of Inertia), a body at rest tends to remain at rest. When the bus suddenly moves forward, the lower body moves with the bus, but the upper body resists motion, causing passengers to lean backward.

(c) speed

Explanation: Momentum (p) is given by p = mv, where m is mass and v is velocity (or speed in a particular direction). Thus, momentum is directly proportional to speed.

(d) a brick

Explanation: Inertia depends on mass. The heavier the object, the greater its inertia. A brick has the highest mass among the given options, so it has the largest inertia.

(d) (a), (b), (c) all correct

Explanation: According to Newton’s First Law, a body remains in its state of rest or uniform motion unless acted upon by an external force. So, all given options are correct.

(a) vector

Explanation: Velocity is a vector quantity because it has both magnitude (speed) and direction. A scalar quantity has only magnitude, such as speed.

(c) acceleration

Explanation: According to Newton’s Second Law, force is given by F = ma. If a force is applied to a body, it will accelerate unless it is perfectly balanced by another force.