Question

A machine delivers power to a body which is proportional to velocity of the body. If the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Power =$F_{\nu }\alpha v$

$\Rightarrow$ mv $\frac{dv}{dt}$ = kv, where k=constant

$\Rightarrow$ m$\frac{dv}{dt}$ = k $\Rightarrow$ mv $\frac{dv}{dx}$ = k

$\Rightarrow$ v dv = $\frac{k}{m}$ dx

Integrating both sides, we get $\frac{v^2}{2}$ = $\frac{k}{m}$x

Hence, Displacement is proportional to the square of instantaneous velocity.