A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = 3 1 t 2 , where t is in seconds. Work done by the force in 2 seconds is:NEET 20

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A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = 3 1 ​ t 2 , where t is in seconds. Work done by the force in 2 seconds is:NEET 2006

TestHub · Accepted Answer

It is given that: s = 3 t 2 ​ Differentiating w.r.t. t we have U = d t d s ​ = 3 2 t ​ Again differentiating w.r.t. t we have a = d t 2 d 2 s ​ = 3 2 ​ Now W = ∫ F d s = ∫ mads W ​ = ∫ m × 3 2 ​ × 3 2 t ​ d t = 9 4 ​ m ∫ t d t = 9 4 ​ m × [ 2 t 2 ​ ] 0 2 ​ = 9 4 ​ × 3 × 2 = 3 8 ​ J ​

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