(D) Power $p$ is defined as the rate of doing work,$p = Fv$.Since $F = ma = m \frac{dv}{dt}$,we can write $p = m v \frac{dv}{dt}$.Rearranging the term

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(D) Power $p$ is defined as the rate of doing work,$p = Fv$.Since $F = ma = m \frac{dv}{dt}$,we can write $p = m v \frac{dv}{dt}$.Rearranging the terms,we get $p \, dt = m v \, dv$.Integrating both sides from $t = 0$ to $t$ and $v = 0$ to $v$:$\int_{0}^{t} p \, dt = \int_{0}^{v} m v \, dv$.$pt = m \left[ \frac{v^2}{2} \right]_{0}^{v}$.$pt = \frac{1}{2} m v^2$.Solving for $v$,we get $v^2 = \frac{2pt}{m}$,which implies $v = \sqrt{\frac{2pt}{m}}$.

Class 11 Physics Work, Energy, Power and Collision Power

Medium

$A$ vehicle of mass $m$ starts from rest and accelerates. If the engine delivers a constant power $p$,what is the velocity of the vehicle at time $t$?

A
$v = \frac{pt}{m}$
B
$v = \frac{2pt}{m}$
C
$v = \sqrt{\frac{pt}{m}}$
D
$v = \sqrt{\frac{2pt}{m}}$

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Work, Energy, Power and Collision

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Power

Two men have a weight ratio of $5 : 3$. If the ratio of the time taken by them to climb stairs is $11 : 9$,find the ratio of their power.

Easy

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Water falls from a waterfall onto the blades of a turbine at a rate of $100 \ kg/s$. If the height of the fall is $100 \ m$,what is the power generated by the turbine?

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$A$ car of mass $2000 \ kg$ is lifted by a crane through a distance of $30 \ m$ in $1 \ minute$. $A$ second crane does the same in $2 \ minutes$. The power supplied by each crane is respectively:

Medium

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Two bodies of mass $m_1$ and $m_2$ $(m_2 > m_1)$ are connected by a light inextensible string which passes through a smooth fixed pulley. The instantaneous power delivered by an external agent to pull $m_1$ with constant velocity $v$ is

Medium

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$A$ vehicle of mass $m$ starts from rest and accelerates. If the engine delivers a constant power $p$,what is the velocity of the vehicle at time $t$?

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Two men have a weight ratio of $5 : 3$. If the ratio of the time taken by them to climb stairs is $11 : 9$,find the ratio of their power.

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