Question

A body starts from rest and is accelerated by a force $F=kt\left(\text{N}\right)$. Options given below show the variation of power with time. Find the correct option related to the above case.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Given $F=kt$
Let mass of car be $m$
Then, $F=ma=kt$
$⟹a=kt/m$
$⟹\frac{dv}{dt}=\frac{kt}{m}$

Integrating both sides:
${\int }_0^{v}dv={\int }_0^t\frac{kt}{m}dt$
(since body starts from rest, $v=0$ at $t=0$
$⟹v=\frac{k{t}^2}{2m}$

Instantaneous power at time $t$, $P=F.v=\frac{kt.k{t}^2}{2m}=\frac{k^2{t}^3}{2m}$
$\therefore P\propto t^3$
This implies that the graph starts from origin and has a cubic curve, hence option (c) is correct.