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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
$\frac{1}{2}\,m\,\frac{v}{{{t_1}}}{\kern 1pt} {t^2}$
B
$m\,\frac{v}{{{t_1}}}{\kern 1pt} {t^2}$
C
$\frac{1}{2}\,{\left( {\frac{{mv}}{{{t_1}}}} \right)^2}{\kern 1pt} {t^2}$
D
$\frac{1}{2}\,m\,\frac{v^2}{{{t^2_1}}}{\kern 1pt} {t^2}$
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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