Question

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

• A. $\sqrt{mk}{t}^{-1/2}$
• B. $\sqrt{2mk}{t}^{-1/2}$-
• C. $\frac{1}{2}\sqrt{mk}{t}^{-1/2}$
• D. $\sqrt{\frac{mk}{2}}{t}^{-1/2}$

Answer 1

The correct option is A $\sqrt{mk}{t}^{-1/2}$

$\frac{dW}{dt}=P$
$\Rightarrow W=Pt$
$\Rightarrow \frac{1}{2}m(v_2^2-v_1^2)=Pt$
$\Rightarrow \frac{1}{2}m{v}^2=Pt$
$\Rightarrow v=\sqrt{\frac{2Pt}{m}}$
$\Rightarrow a=\frac{dv}{dt}=\sqrt{\frac{2P}{m}}\frac{1}{2}{t}^{-\frac{1}{2}}$
$\Rightarrow F=ma=m\sqrt{\frac{2P}{m}}\frac{1}{2}{t}^{-\frac{1}{2}}=\sqrt{mk}{t}^{-\frac{1}{2}}$