Power supplied to a particle of mass 2 kg varies with time as P=(3t2/2)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

Question

Power supplied to a particle of mass 2 kg varies with time as P=(3t2/2)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√2 m/s

Tardigrade Admin · Accepted Answer

From work energy theorem Δ KE =WEnet or Kf-Ki=∫p dt (1/2)mv2-0=∫02( (3/2)t2 ) dt v2=[ (t3/2) ]02 v=2m/s

Q. Power supplied to a particle of mass 2 kg varies with time as $P = \frac{3 t ^{2}}{2} W .$ 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

1 m/s

4 m/s

2 m/s

$22 m / s$

From work energy theorem
$Δ K E = W E_{n e t}$
or $K_{f} - K_{i} = \int p d t$
$\frac{1}{2} m v^{2} - 0 = \int_{0}^{2} (\frac{3}{2} t^{2}) d t$
$v^{2} = [\frac{t ^{3}}{2}]_{0}^{2}$
$v = 2 m / s$

Q. Power supplied to a particle of mass 2 kg varies with time as P=23t2​W. Here t is in second. If velocity of particle at t=0 is v=0, the velocity of particle at time t=2s will be