Question

A particle moves in a straight line with constant acceleration under a constant force $F$. Select the correct alternative(s)

• A. Power developed by this force varies linearly with time
• B. Power developed by this force varies parabolically with time
• C. Power developed by this force varies linearly with displacement
• D. Power developed by this force varies parabolically with displacement

Answer 1

Answer: (A), (D)

The correct options are
A Power developed by this force varies linearly with time
D Power developed by this force varies parabolically with displacement

Acceleration

$m\frac{dv}{dt}=f$ ($f$ is constant)

$dv=\left(\frac{f}{m}\right)dt$

$V=\left(\frac{f}{m}\right)t$

$m\frac{dv}{dt}=F$

$m\frac{dv}{ds}.\frac{ds}{dt}=F$ $[\frac{ds}{dt}=V]$

$Vdv=\left(\frac{f}{m}\right)ds$

$\frac{V^2}{2}=\left(\frac{F}{m}\right)S$

$V=\sqrt{\left(2\frac{F}{m}\right)S}$

Power $=P=F.V$ [$F$ is constant]

$P=F\left(\frac{F}{m}\right)t-k+[k=\frac{F^2}{m}]$

$P$ is linearly depend on time

$P=F.V=F\sqrt{\left(\frac{2F}{m}\right)S}$

$P^2=\left(\frac{2F^3}{m}\right)S$

$S=\lambda P^2$

Power varies parabolically with displacement