An automobile of mass m accelerates from rest. If the engine supplies constant power p, the velocity at time t is given by

v = \frac{p t}{m}

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v = \frac{2 p t}{m}

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v = \sqrt{\frac{p t}{m}}

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v = \sqrt{\frac{2 p t}{m}}

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Solution

The correct option is D $v = \sqrt{\frac{2 p t}{m}}$
P = F.v = m.a.v
a= dv/dt
P/m dt = vdv
$\int_{0}^{t} P / m d t = \int_{0}^{v} v d v$
$P t / m = v^{2} / 2$
$v = \sqrt{2 P t / m}$

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An automobile of mass m accelerates from rest. If the engine supplies constant power p, the velocity at time t is given by

The correct option is D v=√2ptmP = F.v = m.a.va= dv/dtP/m dt = vdv∫t0P/mdt=∫v0vdvPt/m=v2/2v=√2Pt/m

The correct option is D $v = \sqrt{\frac{2 p t}{m}}$
P = F.v = m.a.v
a= dv/dt
P/m dt = vdv
$\int_{0}^{t} P / m d t = \int_{0}^{v} v d v$
$P t / m = v^{2} / 2$
$v = \sqrt{2 P t / m}$