(A) Power is defined as $P = Fv$. Since $F = ma$,we have $P = mav$.Using the definition of acceleration $a = v \frac{dv}{dx}$,we can write $P = m v \f

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${\left( {\frac{{3xP}}{m}} \right)^{1/3}}$

(A) Power is defined as $P = Fv$. Since $F = ma$,we have $P = mav$.Using the definition of acceleration $a = v \frac{dv}{dx}$,we can write $P = m v \frac{dv}{dx} v = m v^2 \frac{dv}{dx}$.Rearranging the terms,we get $P dx = m v^2 dv$.Integrating both sides with initial conditions $x=0$ at $v=0$:$\int_0^x P dx = \int_0^v m v^2 dv$.$Px = m \frac{v^3}{3}$.Solving for $v$,we get $v^3 = \frac{3Px}{m}$,which implies $v = {\left( {\frac{{3xP}}{m}} \right)^{1/3}}$.

Class 11 Physics Work, Energy, Power and Collision Power

Difficult

$A$ car of mass $m$ is driven with constant power $P$. If it starts from rest,find its velocity $v$ after traveling a distance $x$.

A
${\left( {\frac{{3xP}}{m}} \right)^{1/3}}$
B
${\left( {\frac{{2xP}}{m}} \right)^{1/2}}$
C
${\left( {\frac{{xP}}{m}} \right)^{1/3}}$
D
${\left( {\frac{{2xP}}{{3m}}} \right)^{1/4}}$

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Work, Energy, Power and Collision

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The machine gun fires $240$ bullets per minute. If the mass of each bullet is $10 \ g$ and the velocity of the bullets is $600 \ ms^{-1}$,the power (in $kW$) of the gun is

DifficultTS EAMCET 2005

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$A$ $60\; HP$ electric motor lifts an elevator having a maximum total load capacity of $2000\; kg$. If the frictional force on the elevator is $4000\; N$,the speed of the elevator at full load is close to .............. $m/s$.
$(1\; HP = 746\; W, g = 10\; ms^{-2})$

MediumJEE MAIN 2020

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$A$ body is moved along a straight line by an engine which delivers a constant power. The distance moved by the body in time $t$ is proportional to:

EasyTS EAMCET 2023

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$A$ body of mass $m$ is initially at rest. It is subjected to a uniform acceleration such that it acquires a velocity $v$ in time $T$. The instantaneous power supplied to the body as a function of time $t$ is . . . . . . .

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$1\,kWh$ is a unit of power. This statement is true or false? If it is wrong,then correct it.

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$A$ car of mass $m$ is driven with constant power $P$. If it starts from rest,find its velocity $v$ after traveling a distance $x$.

Similar Questions

The machine gun fires $240$ bullets per minute. If the mass of each bullet is $10 \ g$ and the velocity of the bullets is $600 \ ms^{-1}$,the power (in $kW$) of the gun is

$A$ $60\; HP$ electric motor lifts an elevator having a maximum total load capacity of $2000\; kg$. If the frictional force on the elevator is $4000\; N$,the speed of the elevator at full load is close to .............. $m/s$.$(1\; HP = 746\; W, g = 10\; ms^{-2})$

$A$ body is moved along a straight line by an engine which delivers a constant power. The distance moved by the body in time $t$ is proportional to:

$A$ body of mass $m$ is initially at rest. It is subjected to a uniform acceleration such that it acquires a velocity $v$ in time $T$. The instantaneous power supplied to the body as a function of time $t$ is . . . . . . .

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$A$ $60\; HP$ electric motor lifts an elevator having a maximum total load capacity of $2000\; kg$. If the frictional force on the elevator is $4000\; N$,the speed of the elevator at full load is close to .............. $m/s$.
$(1\; HP = 746\; W, g = 10\; ms^{-2})$