# Momentum and Impulse

## Understanding Momentum

**Momentum** in physics is a crucial concept that measures how difficult it is to stop an object in motion. It depends on both the mass and velocity of the object.

**Definition**: Momentum (p) is defined as the product of an object's mass and its velocity, expressed as p = mv.

**Vocabulary**: Momentum is a vector quantity, meaning it has both magnitude and direction.

The direction of momentum is always the same as the direction of motion. Objects with large mass, high speed, or both have significant momentum. Conversely, stationary objects have zero momentum.

**Example**: A 60kg halfback moving east at 9 m/s has a momentum of 540 kg⋅m/s east.

## Impulse and Its Relationship to Momentum

**Impulse** is closely related to momentum and is defined as the change in momentum.

**Definition**: Impulse (J) is calculated as J = Δp = m(vf - vi) = Ft, where F is force and t is time.

An important application of impulse is in reducing the force required to stop an object by increasing the time of contact. This principle is used in various safety features and equipment.

**Example**: Bubble wrap, football gear, running shoes, and car crumple zones all utilize the impulse principle to reduce impact forces.

**Highlight**: To lower the force needed to stop an object, increase the time the objects are in contact.

## Practical Application of Impulse

Consider a scenario where we need to increase the speed of a 1000kg car from 10m/s to 30m/s over a distance of 100m.

- Calculate the impulse: J = 1000(30 - 10) = 20,000 kg⋅m/s
- Determine the time using displacement equations: t = 5s
- Calculate the average force: F = J/t = 20,000/5 = 4000N

Alternatively, we can calculate the acceleration (a = 4 m/s²) and use F = ma to arrive at the same result.