A car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_{0}$ . The instantaneous velocity of this car is proportional to-

t^{1 / 2}

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t^{- 1 / 2}

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t / \sqrt{m}

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t^{2} P_{0}

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Solution

The correct option is A $t^{1 / 2}$
$P_{0} = F . v = m a v$
$P_{0} = m v \frac{d v}{d t}$
$\int m v d v = \int P_{0} d t$
$m \frac{v^{2}}{2} = P_{0} t$
$v \propto \sqrt{t}$

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A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P0. The instantaneous velocity of this car is proportional to-

The correct option is A t1/2P0=F.v=mavP0=mvdvdt∫mvdv=∫P0dtmv22=P0tv∝√t

A car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_{0}$ . The instantaneous velocity of this car is proportional to-

The correct option is A $t^{1 / 2}$
$P_{0} = F . v = m a v$
$P_{0} = m v \frac{d v}{d t}$
$\int m v d v = \int P_{0} d t$
$m \frac{v^{2}}{2} = P_{0} t$
$v \propto \sqrt{t}$