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Momentum is a fundamental concept in physics that describes the quantity of motion possessed by an object. It is a vector quantity, meaning it has both magnitude and direction. Momentum is derived from an object’s mass and velocity and plays a significant role in understanding the behavior of moving objects.

Imagine that you are running on a straight road. If someone asks you to stop, what will happen? Will you be able to stop yourself immediately? No! You will be able to stop yourself only after a second or two. It happens because your body has momentum which tends to take you further with it.

Now, what would have happened if you were running at a greater speed? Yes, you would have taken more time to stop. Also, if you were heavier, even then it would have taken you more time to come to a standstill for the same velocity. This means, the more the mass and the velocity, the greater the momentum.

Thus, Momentum is directly proportional to mass and velocity.

Mathematically it is expressed as the product of mass and velocity. It is denoted by the letter ‘p’. So, we can write the formula of momentum as,

**Momentum (p) = Mass (m) × Velocity (v)**

In this formula, mass (m) is the measure of the amount of matter an object contains, and velocity (v) is the rate at which an object’s position changes with respect to time. By multiplying the mass of an object by its velocity, we can determine its momentum.

## What is the SI unit of momentum?

The SI unit of momentum is kilogram-metre per second (kg·m/s). However, momentum can also be expressed in other units, such as gram-centimetre per second (g·cm/s) or newton-second (N·s), depending on the context.

Now, when a net force is applied, the velocity of the object changes and when velocity changes, its momentum also changes.

So, net force is nothing but the rate of change of momentum.

Therefore,

Net force = (p2 – p1)/t

where, p1 = initial momentum, p2 = final momentum and t = time taken

The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.

### Solved examples on Momentum Formula

**Example 1:** A ball with a mass of 0.5 kilograms is moving with a velocity of 10 meters per second. Calculate its momentum.

Solution:

Given:

Mass (m) = 0.5 kg

Velocity (v) = 10 m/s

To calculate momentum, we use the formula:

Momentum (p) = Mass (m) × Velocity (v)

Substituting the given values into the formula:

p = 0.5 kg × 10 m/s

p = 5 kg·m/s

Therefore, the momentum of the ball is 5 kilogram-metre per second (kg·m/s).

**Example 2:** A truck with a mass of 2000 kilograms is initially at rest. It accelerates uniformly to a velocity of 20 meters per second in a time of 10 seconds. Calculate its momentum.

Solution:

Given:

Mass (m) = 2000 kg

Initial velocity (u) = 0 m/s

Final velocity (v) = 20 m/s

Time (t) = 10 s

To calculate momentum, we use the formula:

Momentum (p) = Mass (m) × Velocity (v)

First, we need to find the change in velocity (Δv) using the formula:

Change in velocity (Δv) = Final velocity (v) – Initial velocity (u)

Δv = 20 m/s – 0 m/s

Δv = 20 m/s

Now, we can substitute the values into the momentum formula:

p = 2000 kg × 20 m/s

p = 40,000 kg·m/s

Therefore, the momentum of the truck is 40,000 kilogram-metre per second (kg·m/s).

**Example 3:** Two objects of masses 2 kilograms and 4 kilograms are moving towards each other. The object with a mass of 2 kilograms has a velocity of 6 meters per second, while the object with a mass of 4 kilograms has a velocity of -3 meters per second. Calculate the total momentum of the system.

Solution:

Given:

Mass of object 1 (m1) = 2 kg

Velocity of object 1 (v1) = 6 m/s

Mass of object 2 (m2) = 4 kg

Velocity of object 2 (v2) = -3 m/s

To calculate momentum, we use the formula:

Momentum (p) = Mass (m) × Velocity (v)

For object 1:

p1 = m1 × v1

p1 = 2 kg × 6 m/s

p1 = 12 kg·m/s

For object 2:

p2 = m2 × v2

p2 = 4 kg × (-3 m/s)

p2 = -12 kg·m/s

The total momentum of the system is the sum of the individual momenta:

Total momentum = p1 + p2

Total momentum = 12 kg·m/s + (-12 kg·m/s)

Total momentum = 0 kg·m/s

Therefore, the total momentum of the system is 0 kilogram-metre per second (kg·m/s).

## FAQ’s on Momentum Formula

### What is momentum?

Momentum is a fundamental concept in physics that represents the quantity of motion possessed by an object. It depends on the object's mass and velocity.

### How is momentum different from velocity?

Velocity is the rate of change of an object's position, including speed and direction. Momentum, on the other hand, is the product of an object's mass and velocity and represents the object's quantity of motion.

### What is the formula for momentum?

The formula for momentum is: Momentum (p) = Mass (m) × Velocity (v)

### What are the SI units of momentum?

The SI unit of momentum is kilogram-metre per second (kg·m/s).

### Is momentum a vector or scalar quantity?

momentum is a vector quantity because it has both magnitude and direction. It follows the same direction as the object's velocity.

### How does momentum relate to Newton's laws of motion?

According to Newton's second law of motion, the rate of change of momentum of an object is equal to the net force acting on it. This relationship forms the basis of understanding the behaviour of objects in motion.