Question

Power supplied to a particle of mass 2kg varies with time as P = 3t^2 /2 .Here t is in second.If the velocity of the particle at t=0 is v=0.The velocity of the particle at the time t=2 s will be?

Answer 1

Answer on Question #73855, Physics – Mechanics, Relativity

Question:

Power supplied to a particle of mass 2kg varies with time as $P = 3t^2 / 2$. Here $t$ is in second. If the velocity of the particle at $t=0$ is $v=0$. The velocity of the particle at the time $t=2$ s will be?

Solution:

The integral of the power is equal to the total energy transferred during this time:

$$E = \int_{t_1}^{t_2} P \cdot dt = \int_{0}^{2} \frac{3t^2}{2} \cdot dt = \left. \frac{t^3}{2} \right|_{0}^{2} = 4 (J)$$

The particle has 4 J of kinetic energy, so the velocity of the particle is:

$$v = \sqrt{\frac{2E}{m}} = 2 (m/s)$$

Answer: $v = 2 \, \text{m/s}$

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