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  4. The kinetic energy acquired by a mass m in travelling distance d, starting from rest, under the action of a constant force is directly proportional to

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Q. The kinetic energy acquired by a mass m in travelling distance $d$, starting from rest, under the action of a constant force is directly proportional to

AIPMTAIPMT 1994Work, Energy and Power

Solution:

$v^{2}=u^{2}+2 a s$
or $v^{2}-u^{2}=2 a s$
or $v^{2}-(0)^{2}=2 \times \frac{F}{m} \times s$
or $v^{2}=\frac{2 F s}{m}$
and K.E. $=\frac{1}{2} m v^{2}=\frac{1}{2} m \times \frac{2 F s}{m}=F S$.
Thus K.E. is independent of $m$ or directly proportional to $m^{0}$.