How do you calculate impulse from change in momentum?

Impulse is calculated by multiplying the change in momentum by the time it takes for this change to occur.

Impulse, often denoted by the letter 'J', is a fundamental concept in physics. It is defined as the change in momentum of an object when a force is applied over a period of time. In other words, impulse is the integral of a force, F, over the time interval, t, for which it acts. The mathematical representation of impulse is J = FΔt.

Momentum, on the other hand, is the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction. The change in momentum, often denoted by the Greek letter 'delta' (Δ), is calculated by subtracting the initial momentum from the final momentum (Δp = p_final - p_initial).

Therefore, if you want to calculate impulse from a change in momentum, you need to know the time over which the change occurred. You then multiply the change in momentum by this time to get the impulse. For example, if a 1 kg object changes its velocity from 5 m/s to 10 m/s over a period of 2 seconds, the change in momentum is (1 kg * 10 m/s) - (1 kg * 5 m/s) = 5 kg*m/s. The impulse is then 5 kg*m/s * 2 s = 10 N*s.

Remember, both impulse and momentum are vector quantities, so they have direction as well as magnitude. When calculating impulse, be sure to take into account the direction of the forces involved. If the force is acting in the opposite direction to the object's motion, it will reduce the object's momentum, and the impulse will be negative. Conversely, if the force is acting in the same direction as the object's motion, it will increase the object's momentum, and the impulse will be positive.