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5.Work, Energy, Power and Collision
normal
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
$ \mathrm{v}=\mathrm{u} +\mathrm{at}_{1} $
$ \mathrm{u}=0 \Rightarrow \mathrm{a}=\frac{\mathrm{v}}{\mathrm{t}_{1}} $
Work $=\Delta \mathrm{k}=\mathrm{k}_{\mathrm{f}}-\mathrm{t}_{\mathrm{i}} $
$=\frac{1}{2} \mathrm{mv}^{2}-\Delta=\frac{1}{2} \mathrm{m}[\mathrm{at}]^{2}=\frac{1}{2} \mathrm{ma}^{2} \mathrm{t}^{2} $
Work $ =\frac{1}{2} \mathrm{m}\left[\frac{\mathrm{v}}{\mathrm{t}_{1}}\right]^{2} \mathrm{t}^{2} $
Standard 11
Physics
