Question

Power supplied to a particle of mass 2 kg varies with time as $P=\frac{{3t}^2}{2}W.$ Here, t is in second. If 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 m/s
• D. $2\sqrt{2}m/s$

Answer 1

Answer: (C)

2 m/s

Power is $P=\frac{dW}{dt}$ given that $P=\frac{3t^2}{2}Watt$

so work $dW=Pdt$ on integrating both sides we get ${\int }_0^{W}dW=\frac{3}{2}{\int }_{t=0}^{t=2}{t}^{2}dt$

we get the work done in this period as $W=\frac{3}{2\times 3}(2^3-0)=4Joule$

So increase in kinetic energy will be $4J$

as the initial KE was $zero$ so new $KE=\frac{m{v}^2}{2}=4$

so velocity $v=\sqrt{\frac{4J\times 2}{2kg}}=2m/s$