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Answer» Given, Mass of body , m = 6 kg displacement is the function of TIME , x = t²/4 ∵ Workdone = force × displacement , but here no any external force ACT on body. ∴ we have to use , Workdone = Change in KINETIC energy
Now, x = t²/4 differentiate x with respect to time , dx/dt = 2t/2 = t/2 We know, dx/dt = velocity of body At t = 2sec, velocity of body , v = 2/2 = 1 m/s So, change in kinetic energy = final kinetic energy - intial kinetic energy of body = 1/2mv² - 0 [because initially body is in rest because velocity of body at t = 0, is 0 ] ∴ change in kinetic energy = 1/2 × 6 × (1)² = 1/2 × 6 = 3 J
Hence , Workdone = 3J
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