A constant power P is applied to a particle of mass m. The distance travelled by the particle when its velocity increases from $v_{1}$ to $v_{2}$ is?(neglect friction)

\frac{3 P}{m} (v_{2}^{2} - v_{1}^{2})

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\frac{m}{3 P} (v_{2} - v_{1})

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\frac{m}{3 P} (v_{2}^{3} - v_{1}^{3})

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\frac{m}{3 P} (v_{2}^{2} - v_{1}^{2})

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Solution

The correct option is C $\frac{m}{3 P} (v_{2}^{3} - v_{1}^{3})$
$P = F V$
$P = m a v$
$P = m v . \frac{d v}{d s} . v$
$\frac{P}{m} . d s = v^{2} . d v$
Integrate both sides under limits $V f r o m v_{1} t o v_{2}$
$d s f r o m 0 t o S$
We get $(\frac{v^{3}}{3}) = \frac{P}{m . s}$
$\frac{1}{3} ({v_{2}}^{3} - {v_{1}}^{3}) = \frac{P}{m . s}$
$\frac{M}{3} P ({v_{2}}^{3} - {v_{1}}^{3}) = S$

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A constant power P is applied to a particle of mass m. The distance travelled by the particle when its velocity increases from v1 to v2 is?(neglect friction)

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