The kinetic energy K of a particle moving in | vedclass

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(A) Given,kinetic energy $K = as^2$.We know that $K = \frac{1}{2}mv^2$,where $m$ is the mass and $v$ is the velocity of the particle.So,$\frac{1}{2}mv

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$2as$

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(A) Given,kinetic energy $K = as^2$.We know that $K = \frac{1}{2}mv^2$,where $m$ is the mass and $v$ is the velocity of the particle.So,$\frac{1}{2}mv^2 = as^2$.Differentiating both sides with respect to time $t$:$\frac{d}{dt}(\frac{1}{2}mv^2) = \frac{d}{dt}(as^2)$$\frac{1}{2}m(2v \frac{dv}{dt}) = a(2s \frac{ds}{dt})$Since $F = m \frac{dv}{dt}$ and $v = \frac{ds}{dt}$,we substitute these into the equation:$mv \frac{dv}{dt} = 2as \frac{ds}{dt}$$F \cdot v = 2as \cdot v$$F = 2as$.

The kinetic energy $K$ of a particle moving in a straight line depends upon the distance $s$ as $K = as^2$. The force acting on the particle is

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