The speed v reached by a car of mass m in travelling a distance x, driven with constant power P, is given by

v = \frac{3 x p}{m}

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v = ⟮ \frac{3 x p}{m} ⟯^{1 / 2}

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v = ⟮ \frac{3 x p}{m} ⟯^{1 / 3}

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v = ⟮ \frac{3 x p}{m} ⟯^{2}

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Solution

The correct option is A $v = ⟮ \frac{3 x p}{m} ⟯^{1 / 3}$
$P = f . v$
$\Rightarrow m (d v / d t) v = P$
$\Rightarrow m (d v / d s) (d s / d t) V = P$
$\Rightarrow m (d v / d s) v^{2} = P$
$\Rightarrow m v^{2} d v = P d s$
Integrating with limits $v = 0$ to $v$ and $s = 0$ to $s = x$ we get,
$V = (3 x P / m)^{1 / 3}$

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