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

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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

$\frac{1}{2}{\left( {\frac{{m\,v}}{{{t_1}}}} \right)^2}{t^2}$

D

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

Solution

(d) Work done =$F \times s = ma \times \frac{1}{2}a{t^2}$ $\left[ {{\rm{from }}s = ut + \frac{1}{2}a{t^2}} \right]$

$\therefore W$=$\frac{1}{2}m{a^2}{t^2}$$ = \frac{1}{2}m{\left( {\frac{v}{{{t_1}}}} \right)^2}{t^2}$

$\left[ {{\rm{As }}a = \frac{v}{{{t_1}}}} \right]$

Standard 11

Physics

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