Power applied to a particle varies with time as $P = (3t^{2} - 2t + 1)$ watt, where $t$ is in second. Find the change in its kinetic energy between $t = 2$ s and $t = 4$ s

Question

Dr. Abubacker · Accepted Answer

(b) $P = 3t^{2} - 2t + 1 = \frac{dE}{dt}$
$	herefore\ dE = (3t^{2} - 2t + 1)dt$
$E = \int_{t = 2s}^{t = 4s}{(3t^{2} - 2t + 1)dt}$
$= \left\lbrack \frac{3t^{3}}{3} - \frac{2t^{2}}{2} + t ightbrack_{t = 2s}^{t = 4s}$
$= \lbrack\left( 4^{3} - 2^{3} ight) - \left( 4^{2} - 2^{2} ight) + (4 - 2)brack$
$E = 56 - 12 + 2 = 46\ J$

Q. Power applied to a particle varies with time as $P = (3t^{2} - 2t + 1)$ watt, where $t$ is in second. Find the change in its kinetic energy between $t = 2$ s and $t = 4$ s

Explanation

Reviewed by Dr. Abubacker

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