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

2 a s

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2 m a s

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2 a

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\sqrt{a s^{2}}

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Solution

The correct option is A $2 a s$
Velocity, $v = \frac{d i s p l a c e m e n t}{t i m e} = \frac{s}{t}$

Acceleration, $= \frac{s}{t^{2}}$

Kinetic energy,

$K . E = \frac{1}{2} m a s s \times v e l o c i t y^{2} = a s^{2}$

$m a s s = \frac{2 a s^{2}}{s^{2} / t^{2}} = 2 a t^{2}$

Force, $F = m a s s \times a c c e l e r a t i o n = 2 a t^{2} \frac{s}{t^{2}} = 2 a s$

Hence, force is $2 a s$

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