Question

Power supplied to a particle of mass 2 kg varies with time as $P=\frac{3t^2}{2}$ watt, where t is in second. If the velocity of particle at t = 0 is v = 0, the velocity of particle at time t = 2 s will be

• A. 1 m/s
• B. 4 m/s
• C. $2\sqrt{2}$ m/s
• D. $2$ m/s

Answer 1

The correct option is D $2$ m/s

From work-energy theorem,
Work done = change in kinetic energy

$\int Pdt=K_{final}-K_{initial}$

${\int }_0^2\left(\frac{3t^2}{2}\right)dt=\frac{1}{2}m{v}^2-0$

$\frac{3}{2}{\left[\frac{t^3}{3}\right]}_0^2=\frac{1}{2}\left(2\right)v^2$

$v=2m/s$