Power supplied to a particle of mass 2 kg varies with time as P=t2 / 2 watt, where t is in second. If velocity of particle at t=0 is v=0, the velocity of particle at t=2 s will be

Question

Power supplied to a particle of mass 2 kg varies with time as P=t2 / 2 watt, where t is in second. If velocity of particle at t=0 is v=0, the velocity of particle at t=2 s will be (A) 1 ms -1 (B) 4 ms -1 (C) 2 √(2/3) ms -1 (D) 2 √2 ms -1

Tardigrade Admin · Accepted Answer

From work-energy theorem, Δ KE =W text net Kf-Ki =∫ P d t (1/2) m v2-0 =∫ limits02((t2/2)) d t or (1/2)(2) v2 =(1/2)[(t3/3)]02 v=2 √(2/3) ms -1

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

$1 m s^{- 1}$

$4 m s^{- 1}$

$2 \frac{2}{3} m s^{- 1}$

$22 m s^{- 1}$

From work-energy theorem, $Δ K E = W_{net}$
$K_{f} - K_{i} = \int P d t$
$\frac{1}{2} m v^{2} - 0 = 0 \int 2 (\frac{t ^{2}}{2}) d t$
or $\frac{1}{2} (2) v^{2} = \frac{1}{2} [\frac{t ^{3}}{3}]_{0}^{2}$
$v = 2 \frac{2}{3} m s^{- 1}$

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

1ms−1

4ms−1

232​​ms−1

22​ms−1