The relation between the displacement x and the time t for a body of mass 2kg moving under the action of force is given by x=t3/3 , where x is in metre and t in second , calculate the work done by body in first 2 seconds.
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M = 2 kg
x = t^3 /3 m/s , dx = t² dt
v = dx/dt = t²
a = dv/dt = 2 t
force = m a = 4 t
dW = force * dx = 4 t dx = 4 t³
Work done during t = 0 to 2 sec is found by integration
W = [ t^4 ]_0 ^2 = 16 J
x = t^3 /3 m/s , dx = t² dt
v = dx/dt = t²
a = dv/dt = 2 t
force = m a = 4 t
dW = force * dx = 4 t dx = 4 t³
Work done during t = 0 to 2 sec is found by integration
W = [ t^4 ]_0 ^2 = 16 J
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