Question

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

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

Answer 1

Answer: (C)

From work energy theorem, Δ K.E. = W_net
$\text{K}_{\text{f}} - \text{K}_{\text{i}} = ∫ \text{P} \text{dt}$
$\frac{1}{2} \left(\text{mv}\right)^{2} - 0 = ∫_{0}^{2} \left(\frac{3}{2} \left(\text{t}\right)^{2}\right) \text{dt}$
$\frac{1}{2} \left(\left(2\right) \text{v}\right)^{2} = \frac{3}{2} \left[\frac{\left(\text{t}\right)^{3}}{3}\right]_{0}^{2} = 4$
v = 2 m/s