Question

A body starts moving under the action of a constant force along the straight line. The instantaneous power $\left(P\right)$ developed by this force with time $\left(t\right)$ is correctly represented by

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Given that,
force $\left(F\right)=$ constant
Let, $m=$ mass of the body
$a=$ acceleration of body due to force $F$
$\therefore a=\frac{F}{m}$
and $v=u+at$
$v=u+\left(\frac{F}{m}\right)t$ (as $u=0$)
$v=\frac{F}{m}t$
$\therefore$ Instantaneous power $\left(P\right)=F.v$
$=F.\frac{F}{m}t=\left(\frac{F^2}{m}\right)t$ (Both $F$ & $v$ have same direction)
$\Rightarrow P=\frac{F^2}{m}t$
$\Rightarrow P$ ∝t ($\because$ $F$ and $m$ is constant)
i.e. P-t graph is a straight line passing through origin.

Tips: For constant force, rate of power generation or dissipation is constant for a given mass.