Impulse is a fundamental concept in physics that describes the effect of a force acting over a period of time. It is defined as the change in momentum of an object and is equal to the average force multiplied by the time interval over which the force acts. Impulse plays a crucial role in understanding collisions, explosions, and other phenomena involving rapid changes in momentum.

The formula for impulse is:

\[ J = F\Delta t = m\Delta v = m(v_f - v_i) \]

Where:

- \( J \) is the impulse (in Newton-seconds, N·s)
- \( F \) is the average force (in Newtons, N)
- \( \Delta t \) is the time interval (in seconds, s)
- \( m \) is the mass of the object (in kilograms, kg)
- \( \Delta v \) is the change in velocity (in meters per second, m/s)
- \( v_f \) is the final velocity (in m/s)
- \( v_i \) is the initial velocity (in m/s)

To calculate impulse and change in velocity:

- Identify the given values: mass (\(m\)), initial velocity (\(v_i\)), and final velocity (\(v_f\)).
- Calculate the change in velocity: \[ \Delta v = v_f - v_i \]
- Calculate the impulse: \[ J = m\Delta v \]

Let's consider an example where a 2 kg object changes velocity from 3 m/s to 7 m/s:

Calculations:

- Change in velocity: \(\Delta v = 7 \text{ m/s} - 3 \text{ m/s} = 4 \text{ m/s}\)
- Impulse: \(J = 2 \text{ kg} \times 4 \text{ m/s} = 8 \text{ N·s}\)

This diagram illustrates the initial and final states of the object, with the impulse represented by the yellow arrow between them.

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