The velocity v reached by a car of mass m at | vedclass

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(C) Power $P$ is defined as the rate of change of kinetic energy: $P = \frac{dK}{dt} = \frac{d}{dt} (\frac{1}{2} m v^2) = m v \frac{dv}{dt}$.Since $a

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$v^3 \propto \frac{2 P}{m}$

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(C) Power $P$ is defined as the rate of change of kinetic energy: $P = \frac{dK}{dt} = \frac{d}{dt} (\frac{1}{2} m v^2) = m v \frac{dv}{dt}$.Since $a = \frac{dv}{dt}$,we have $P = m v a = m v (v \frac{dv}{dx}) = m v^2 \frac{dv}{dx}$.Rearranging the terms: $v^2 dv = \frac{P}{m} dx$.Integrating both sides: $\int_0^v v^2 dv = \int_0^x \frac{P}{m} dx$.$\frac{v^3}{3} = \frac{P x}{m}$.Thus,$v^3 = \frac{3 P x}{m}$.Since $P$,$m$,and $x$ (at a certain distance) are related,we find $v^3 \propto \frac{P}{m}$.

The velocity $v$ reached by a car of mass $m$ at a certain distance from the starting point,driven with constant power $P$,is such that:

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