Question

Power supplied to a particle of mass 2 kg varies with time as $p=\frac{3t^2}{2}$ watt. Here 't' is in second. If velocity of particle at t = 0 is v = 0. The velocity of particle at time t = 2 second will be

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

Answer 1

The correct option is C 2 m/s

$k_f-k_i={\int }_0^{2}Pdt\Rightarrow \frac{1}{2}m{v}^2={\int }_0^2\frac{3}{2}{t}^{2}dt\Rightarrow v^2={\left[\frac{t^3}{2}\right]}_0^2\Rightarrow v=2m/s$