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(D) Given: Mass $m = 2000 \ kg$,Power $P = 10 \ kW = 10000 \ W$,Time $t = 10 \ s$.We know that Power $P = F \cdot v = (m \cdot a) \cdot v = m \cdot \f

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$10$

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(D) Given: Mass $m = 2000 \ kg$,Power $P = 10 \ kW = 10000 \ W$,Time $t = 10 \ s$.We know that Power $P = F \cdot v = (m \cdot a) \cdot v = m \cdot \frac{dv}{dt} \cdot v$.So,$P \cdot dt = m \cdot v \cdot dv$.Integrating both sides from $t = 0$ to $t = 10 \ s$ and $v = 0$ to $v = v$:$\int_{0}^{10} P \, dt = \int_{0}^{v} m \cdot v \, dv$.$P \cdot t = \frac{1}{2} \cdot m \cdot v^2$.$10000 	imes 10 = \frac{1}{2} 	imes 2000 	imes v^2$.$100000 = 1000 	imes v^2$.$v^2 = 100$.$v = 10 \ m \ s^{-1}$.

$A$ car of mass $2000 \ kg$ is accelerating from rest. If its engine is supplying a constant power of $10 \ kW$,then the velocity of the car at a time of $10 \ s$ is: (in $m \ s^{-1}$)

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