(B) The instantaneous power $P_0$ is given by $P_0 = Fv$.Since $F = ma = m(dv/dt)$,we can write $P_0 = mv(dv/dt)$.Rearranging the terms,we get $P_0 dt

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(B) The instantaneous power $P_0$ is given by $P_0 = Fv$.Since $F = ma = m(dv/dt)$,we can write $P_0 = mv(dv/dt)$.Rearranging the terms,we get $P_0 dt = mv dv$.Integrating both sides from $t=0$ to $t$ and $v=0$ to $v$:$\int_0^t P_0 dt = \int_0^v mv dv$$P_0 t = \frac{1}{2}mv^2$.Solving for $v$,we get $v = \sqrt{\frac{2P_0 t}{m}}$.Therefore,$v \propto \sqrt{t}$ or $v \propto t^{1/2}$.

Class 11 Physics Work, Energy, Power and Collision Power

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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 $P_0$. The instantaneous velocity of this car is proportional to

AIPMT 2012 All AIPMT

A
$t^2P_0$
B
$t^{1/2}$
C
$t^{3/2}$
D
$t/\sqrt{m}$

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Work, Energy, Power and Collision

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$A$ particle of mass $0.2 \ kg$ is moving in one dimension under a force that delivers a constant power $0.5 \ W$ to the particle. If the initial speed of the particle is zero,the speed (in $m/s$) after $5 \ s$ is:

MediumIIT 2013

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From a waterfall,water is falling down at the rate of $100 \ kg/s$ on the blades of a turbine. If the height of the fall is $100 \ m$,then the power delivered to the turbine is approximately equal to ........... $kW$.

Medium

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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 $P_0$. The instantaneous velocity of this car is proportional to

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$A$ particle of mass $0.2 \ kg$ is moving in one dimension under a force that delivers a constant power $0.5 \ W$ to the particle. If the initial speed of the particle is zero,the speed (in $m/s$) after $5 \ s$ is:

$A$ box is moved along a straight line by a machine delivering constant power. The distance moved by the body in time $t$ is proportional to

$A$ body of mass $m$ starts from rest and moves with uniform acceleration such that it attains a velocity $v$ in time $T$. The instantaneous power delivered to the body as a function of time $t$ is given by:

From a waterfall,water is pouring down at the rate of $100 \,kg/s$ on the blades of a turbine. If the height of the fall is $100 \,m$,the power delivered to the turbine is approximately equal to .......... $kW$.

From a waterfall,water is falling down at the rate of $100 \ kg/s$ on the blades of a turbine. If the height of the fall is $100 \ m$,then the power delivered to the turbine is approximately equal to ........... $kW$.

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