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  4. The kinetic energy K of a particle moving in a straight line depends upon the distance s as K=as2 The force acting on the particle is

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Q. The kinetic energy $K$ of a particle moving in a straight line depends upon the distance $s$ as $K=as^{2}$ The force acting on the particle is

AFMCAFMC 2012

Solution:

Velocity, $v =\frac{\text { displacement }}{\text { time }}=\frac{ s }{ t }$
Acceleration, $=\frac{ s }{ t ^{2}}$
Kinetic energy,
$K \cdot E =\frac{1}{2}$ mass $\times$ velocity $^{2}= as ^{2}$
mass $=\frac{2 as ^{2}}{ s ^{2} / t ^{2}}=2 at ^{2}$
Force, $F=$ mass $\times$ acceleration
$=2 at ^{2} \frac{ s }{ t ^{2}}=2 as$
Hence, force is $2 as$