Power delivered to a mass is P = (3t^2 - 2t + | vedclass

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(A) The power $P$ is defined as the rate of change of work done,which is equal to the rate of change of kinetic energy: $P = \frac{dK}{dt}$.Integratin

Vedclass · Accepted Answer

$46$

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(A) The power $P$ is defined as the rate of change of work done,which is equal to the rate of change of kinetic energy: $P = \frac{dK}{dt}$.Integrating this expression with respect to time $t$ gives the change in kinetic energy $\Delta K = \int_{t_1}^{t_2} P \, dt$.Given $P = 3t^2 - 2t + 1$,we integrate from $t = 2 	ext{ s}$ to $t = 4 	ext{ s}$:$\Delta K = \int_{2}^{4} (3t^2 - 2t + 1) \, dt$.Evaluating the integral:$\Delta K = [t^3 - t^2 + t]_{2}^{4}$.Substituting the upper limit $(t = 4)$:$K(4) = 4^3 - 4^2 + 4 = 64 - 16 + 4 = 52 	ext{ J}$.Substituting the lower limit $(t = 2)$:$K(2) = 2^3 - 2^2 + 2 = 8 - 4 + 2 = 6 	ext{ J}$.Therefore,the change in kinetic energy is $\Delta K = K(4) - K(2) = 52 - 6 = 46 	ext{ J}$.

Power delivered to a mass is $P = (3t^2 - 2t + 1) \text{ W}$. The change in kinetic energy from $t = 2 \text{ s}$ to $t = 4 \text{ s}$ is $...... \text{ J}$.

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