A particle of mass m is initially at rest at | vedclass

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Question

$\frac{ dK }{ dt }=\gamma t$

$K =\frac{1}{2} mv ^2$

$\frac{ dK }{ dt }=\frac{1}{2} m 	imes 2 v \frac{ dv }{ dt }=\gamma t$

$v \frac{ dv }{ d

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Vedclass · Answer

$\frac{ dK }{ dt }=\gamma t$

$K =\frac{1}{2} mv ^2$

$\frac{ dK }{ dt }=\frac{1}{2} m 	imes 2 v \frac{ dv }{ dt }=\gamma t$

$v \frac{ dv }{ dt }=\frac{\gamma t }{ m }$

$\int vdv =\frac{\gamma}{ m } \int tdt$

$\frac{ v ^2}{2}=\frac{\gamma}{ m } \cdot \frac{ t ^2}{2}$

$v =\sqrt{\frac{\gamma}{ m }} \cdot t 	ext { (proportional to time) }$

$a =\frac{ dv }{ dt }=\sqrt{\frac{\gamma}{ m }}$

$F = ma =\sqrt{\gamma m } 	ext { (constant) }$

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