Force on particle driven by constant power – Rankers Physics

Power: Practice Problem & Solution

A particle of mass $m$ is driven by a machine that delivers a constant power $k$ watts. If the particle starts from rest the force on the particle at time $t$ is: (2015)
$\sqrt{mkt^{-1}}$
$\sqrt{2mkt^{-1}}$
$\frac{1}{2}\sqrt{mkt^{-1}}$
$\sqrt{\frac{mk}{2}} t^{-1/2}$

Solution Explained:

To solve this problem, we apply the core principles of Power. Understanding the underlying formula is key to arriving at the correct answer below:

Using constant power $P = Fv$ and $P = mv\frac{dv}{dt}$, integrating gives velocity $v = \sqrt{\frac{2kt}{m}}$. Since force $F = \frac{P}{v}$, substituting velocity yields $F = \sqrt{\frac{mk}{2}} t^{-1/2}$.

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