Question

Force acting on a particle moving in a straight line varies with the velocity of the particle as $F = KV ^{-2},$ where $K$ is constant. The work done by this force in time $t$ is:

• A. $KVt$
• B. $K^{2} V^{2} t^{2}$
• C. $K^{2} V t$
• D. $\frac{3 Kt }{2 V }$

Answer 1

Answer: (D)

$m \frac{ dv }{ dt }= Kv ^{-2}$
$\int m \left( v ^{2} dv \right)=\int Kdt$
$m \left(\frac{ v ^{3}}{3}\right)= Kt$
$\frac{1}{2} m v^{2}=\frac{3}{2} \frac{K t}{v}$