Work done in time t on a body of mass m which | vedclass

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(D) Given that the body starts from rest,the initial velocity $u = 0$.Using the equation of motion $v = u + at_1$,we find the acceleration $a = \frac{

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$\frac{1}{2}m\frac{v^2}{t_1^2}t^2$

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(D) Given that the body starts from rest,the initial velocity $u = 0$.Using the equation of motion $v = u + at_1$,we find the acceleration $a = \frac{v}{t_1}$.The velocity at any time $t$ is given by $v(t) = at = \left(\frac{v}{t_1}\right)t$.The work done on the body is equal to the change in its kinetic energy: $W = \Delta K = \frac{1}{2}m[v(t)]^2 - 0$.Substituting $v(t)$,we get $W = \frac{1}{2}m\left(\frac{v}{t_1}t\right)^2$.Thus,$W = \frac{1}{2}m\frac{v^2}{t_1^2}t^2$.

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by

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