Question

Impulse can be defined as

• A. The change in momentum
• B. The rate of change of momentum
• C. A constant force applied over a distance
• D. Energy transferred over time

Hint:

Impulse-Momentum Theorem. Impulse (\(\vec{J = \int \vec{F dt\)) equals the change in momentum (\(\Delta \vec{p = m\vec{v_f - m\vec{v_i\)). Force is the rate of change of momentum.

Answer 1

The Correct Option is A

Impulse (\(\vec{J}\)) is defined as the integral of force (\(\vec{F}\)) over the time interval (\(\Delta t\)) during which it acts: $$ \vec{J} = \int_{t_1}^{t_2} \vec{F} dt $$ According to Newton's second law, force is the rate of change of momentum (\(\vec{p}\)): \( \vec{F} = \frac{d\vec{p}}{dt} \).
Substituting this into the impulse integral: $$ \vec{J} = \int_{t_1}^{t_2} \frac{d\vec{p}}{dt} dt = \int_{p_1}^{p_2} d\vec{p} = \vec{p}_2 - \vec{p}_1 = \Delta \vec{p} $$ This is the Impulse-Momentum Theorem, which states that the impulse applied to an object is equal to the change in its momentum.
Option (1) correctly defines impulse as the change in momentum.
Option (2) defines force.
Option (3) relates to work.
Option (4) relates to power or energy transfer rate.