In introductory mechanics, which statement best defines the impulse delivered to an object by a force over a time interval?

• A. The work done by the force, given by $W=\int F dx$.
• B. The average force during the interval, given by $F_{\mathrm{avg}}=\frac{\Delta p}{\Delta t}$.
• C. The object's momentum at an instant, given by $p=mv$.
• D. The change in momentum of the object, equal to $J=\int F dt$ (and for constant force $J=F\Delta t$).

Answer: (D)

Verified step by step guidance

1. Understand that impulse is a concept in mechanics that relates the effect of a force applied over a time interval to the change in an object's momentum.
2. Recall the definition of momentum, which is given by the equation \(p = m v\), where \(m\) is mass and \(v\) is velocity.
3. Recognize that impulse \(J\) is defined as the integral of force over the time interval during which the force acts: \(J = \int F \, d t\).
4. Know that impulse is directly related to the change in momentum of the object, expressed as \(J = \Delta p = p_{final} - p_{initial}\).
5. For a constant force, simplify the impulse calculation to \(J = F \Delta t\), where \(\Delta t\) is the duration of the force application.