In an impact, the average force of impact is most directly related to which impulse relationship?

• A. $F_{\text{avg}}=\frac{p}{t}$
• B. $F_{\text{avg}}=\Delta p\Delta t$
• C. $F_{\text{avg}}=\frac{\Delta p}{\Delta t}$
• D. $F_{\text{avg}}=\frac{\Delta t}{\Delta p}$

Answer: (C)

Verified step by step guidance

1. Understand that impulse is defined as the change in momentum, which can be written as \(\Delta p = p_{final} - p_{initial}\).
2. Recall that the average force during an impact is related to how quickly the momentum changes over the time interval of the impact.
3. Express the average force \(F_{avg}\) as the ratio of the change in momentum to the change in time: \(F_{avg} = \frac{\Delta p}{\Delta t}\).
4. Recognize that this formula shows the direct relationship between average force and impulse, where impulse is the product of average force and time interval: \(J = F_{avg} \times \Delta t = \Delta p\).
5. Conclude that the correct impulse relationship for average force is \(F_{avg} = \frac{\Delta p}{\Delta t}\), meaning the average force equals the change in momentum divided by the time over which the change occurs.