In classical mechanics, impulse is defined as the product of the average force acting on a body and the time interval for which it acts. Impulse is exactly equal to which of the following physical quantities?

Introduction / Context:

Impulse is a useful concept in mechanics, especially in situations where forces act for short time intervals, such as collisions or hitting a ball with a bat. Rather than dealing with large, rapidly changing forces directly, we work with the impulse delivered. This question asks you to recall the fundamental relationship between impulse and momentum, a key result of Newton second law in its more general form.

Given Data / Assumptions:

• Impulse J is defined as J = F_avg * Δt for a constant average force F_avg acting for time Δt.
• Momentum p of a body is defined as p = m * v.
• Newton second law can be written in terms of momentum as F = dp / dt.
• We consider the net impulse acting on a body during a given time interval.

Concept / Approach:

Starting from the momentum form of Newton second law, F = dp / dt, we can rearrange to dp = F * dt. Integrating both sides over a time interval gives the total change in momentum equal to the integral of force with respect to time. For a constant or average force, this integral reduces to J = F_avg * Δt. Therefore, the impulse delivered to a body equals the change in its momentum. This is known as the impulse momentum theorem. It is not equal to change in force, velocity or acceleration by themselves, although these may all change during the interaction.

Step-by-Step Solution:

Verification / Alternative check:

Consider a ball of mass m at rest that is struck by a bat and leaves with velocity v. The initial momentum is 0 and the final momentum is m * v, so the change in momentum is m * v. The impulse delivered by the bat, calculated as average force multiplied by contact time, must equal this change in momentum. Experiments with force sensors in sports science confirm this link between the impulse and the resulting change in ball momentum.

Why Other Options Are Wrong:

Option B (change in force): Impulse is not about how much the force value itself changes, but about the combined effect of force and time on momentum.

Option C (change in velocity): Change in velocity is related, but impulse equals change in momentum, which includes mass as well. For the same change in velocity, a more massive object has a larger change in momentum.

Option D (change in acceleration): Acceleration describes how velocity changes, but impulse is related to momentum directly, not to acceleration.

Option E (product of mass and displacement): That product is not a standard mechanical quantity and is not equal to impulse.

Common Pitfalls:

Some students confuse impulse with force or with change in velocity because they see the equation F = m * a and then think in terms of acceleration. The safest approach is to remember the impulse momentum theorem explicitly: impulse equals change in momentum. Whenever force acts over time and you need the overall effect on motion, think about how momentum changes rather than focusing only on instantaneous force values.

Final Answer:

Impulse is equal to the change in momentum of the body.