A body of mass 6 kg is acted upon by a force which causes a displacement in it given by metre where t is the time in second. The work done by the force is 2 seconds is

JEE MainPhysicsModerateWork Power & Energy

A body of mass 6 kg is acted upon by a force which causes a
displacement in it given by $x = \frac{t^{2}}{4}$ metre where t is the
time in second. The work done by the force is 2 seconds is

Show answer and solution

The velocity of the body a time t is given by

= \frac{dx}{dt} = \frac{d}{dt}(\frac{t^{2}}{4}) = \frac{t}{2}

t = 0, = u = 0\ and\ t = 2s, = 1{ms}^{- 1}

, Now, work done =
increase in KE

= \frac{1}{2}m - \frac{1}{2}mu^{2} = \frac{1}{2}m - 0

= \frac{1}{2}m = \frac{1}{2} \times 6 \times (1)^{2} = 3J

Source: Grass-G / P-16 Physics paper 25 Nov First.docx

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