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Question 2.9: Power Needs of a Car to Accelerate Determine the power requi...

Power Needs of a Car to Accelerate

Determine the power required to accelerate a 900-kg car shown in Fig. 2–38 from rest to a velocity of 80 km/h in 20 s on a level road.

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The power required to accelerate a car to a specified velocity is to be determined.

Analysis      The work needed to accelerate a body is simply the change in the kinetic energy of the body,

\begin{aligned}W_{a} &=\frac{1}{2} m\left(V_{2}^{2}-V_{1}^{2}\right)=\frac{1}{2}(900 \mathrm{~kg})\left[\left(\frac{80,000 \mathrm{~m}}{3600 \mathrm{~s}}\right)^{2}-0^{2}\right]\left(\frac{1 \mathrm{~kJ} / \mathrm{kg}}{1000 \mathrm{~m}^{2} / \mathrm{s}^{2}}\right) \\&=222 \mathrm{~kJ}\end{aligned}

The average power is determined from

\dot{W}_{a}=\frac{W_{a}}{\Delta t}=\frac{222 \mathrm{~kJ}}{20 \mathrm{~s}}=11.1 \mathrm{~kW} \quad \text { (or }14.9  hp)

Discussion      This is in addition to the power required to overcome friction, rolling resistance, and other imperfections.

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