Question

Force acting on a particle moving in a straight line with velocity of particle as $F=\alpha /V$ Where ${}^{\prime }{\alpha }^{\prime }$ is constant.
The work done by this force in time interval $△t$ is :

• A. $\alpha \Delta t$
• B. $\frac{1}{2}\alpha \Delta t$
• C. $2\alpha \Delta t$
• D. $\alpha \gamma \Delta t$

Answer 1

The correct option is A $\alpha \Delta t$

$F=ma=\frac{\alpha }{V}$

Or $m\left(\frac{dv}{dt}\right)=\frac{\alpha }{t}=mvdv=adt$

By integrating

$m(\frac{V_2^2}{2}-\frac{V_1^2}{1})=\alpha △t$

Because change in Kinetic energy = work done

So( A) is correct answer