Question

A constant force F is applied on a body. The power (P) generated is related to the time elapsed (t) as

• A. $P \propto t^{2}$
• B. $P \propto t$
• C. $P \propto \sqrt{t}$
• D. $P \propto t^{3/2}$

Answer 1

Answer: (B)

$P \propto t$

Answer 2

$F = \frac{mdv}{dt}$ ∴ F dt = mdv ⇒ $v = \frac{F}{m}t$

Now P = F × v $= F \times \frac{F}{m}t = \frac{F^{2}t}{m}$

If force and mass are constants then P ∝ t.