A car of mass m has engine which can deliver power P. The maximum speed that the car, can attain in t seconds is?

\frac{m v}{2 p}

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2 \sqrt{\frac{P t}{m}}

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\sqrt{\frac{2 P t}{m}}

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\sqrt{\frac{P t}{m}}

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Solution

The correct option is A $\frac{m v}{2 p}$
Work, W, is Power, P, multiplied by time, t. The work done by the engine in time t is thus W = P t.

The work energy principle is that the work done on a system is equal to the change in energy, ΔE, of the system.

Since there is no potential energy in this problem, the change in energy is just the change in kinetic energy.

That is $Δ E = \frac{1}{2} m \times v^{2} - 0 = (\frac{1}{2}) m v 2.$

$\frac{1}{2} m \times v^{2} = \frac{m v}{2 p}$

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