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:

Question

Aicharya · Accepted Answer

$\begin{aligned} & F v=	ext{constant}=k \ & 	ext{So}, \ & \frac{m dv}{d t} v=k \ \Rightarrow & \int v dv=\int \frac{k}{m} dt \ \Rightarrow & \frac{v^2}{2}=\frac{k}{m} t \ \Rightarrow & v=\sqrt{\frac{2 k}{m} t} \end{aligned}$ Now, $\begin{aligned} & F=\frac{m dv}{d t} \ & =m \sqrt{\frac{2 k}{m}} \frac{1}{2} t^{-\frac{1}{2}} \ & =\sqrt{\frac{m k}{2}} t^{-\frac{1}{2}} \end{aligned}$

A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts…

Solution