Work done in time t on a body of mass m which is accelerated from rest to a speed v in time t₁ as

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5.Work, Energy, Power and Collision

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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

A

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

B

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

C

$\frac{1}{2}{\left( {\frac{{mv}}{{{t_1}}}} \right)^2}{t^2}$

D

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

Solution

We know acceleraton $= v/a$

Force $=m \cdot a=m \cdot \frac{v}{t_{1}}$

Distance covered in time $t$

$s=\frac{1}{2} a t^{2}=\frac{1}{2}\left(\frac{v}{t_{1}}\right) t^{2}$

Work done $=$ force $\times$ distance

$=\frac{m v}{t_{1}} \times \frac{1}{2}\left(\frac{v}{t_{1}}\right) t^{2}=\frac{1}{2} m\left(\frac{v}{t_{1}}\right)^{2} t^{2}$

Standard 11

Physics

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