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:

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) K2 V2 t2 (C) K2 V t (D) (3 Kt /2 V )

Tardigrade Admin · Accepted Answer

m ( dv / dt )= Kv -2 ∫ m ( v 2 dv )=∫ Kdt m (( v 3/3))= Kt (1/2) m v2=(3/2) (K t/v)

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

$K V t$

$K^{2} V^{2} t^{2}$

$K^{2} V t$

$\frac{3 K t}{2 V}$

$m \frac{d v}{d t} = K v^{- 2}$
$\int m (v^{2} d v) = \int K d t$
$m (\frac{v ^{3}}{3}) = K t$
$\frac{1}{2} m v^{2} = \frac{3}{2} \frac{K t}{v}$

Q. 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:

KVt

K2V2t2

K2Vt

2V3Kt​