Which of the following expressions correctly represents the average power delivered by a force acting on an object over a time interval $\Delta t$ with work done $W$?

• A. $P=\frac{\Delta }{t}W$
• B. $P=W\times \Delta t$
• C. $P=\frac{W}{\Delta t}$
• D. $P=\frac{\Delta }{t}$

Answer: (C)

Verified step by step guidance

1. Recall the definition of average power, which is the rate at which work is done over a time interval. Mathematically, average power \(P\) is given by the total work done \(W\) divided by the time interval \(\Delta t\) during which the work is done.
2. Write the formula for average power as \(P = \frac{W}{\Delta t}\), where \(W\) is the work done and \(\Delta t\) is the time interval.
3. Understand that the expression \(P = \Delta t \times W\) is incorrect because power is not the product of work and time, but rather work per unit time.
4. Also note that \(P = \frac{\Delta t}{W}\) is incorrect because it inverts the relationship, dividing time by work instead of work by time.
5. Therefore, the correct expression for average power delivered by a force over a time interval \(\Delta t\) with work done \(W\) is \(P = \frac{W}{\Delta t}\).