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The velocity v of a body moving along a straight line varies with time t as v=2t^2*e^-t,where v is in m/s and t is in second . The acceleration of body is zero at t=?
v=2t2etthena=2tet(t+2)a=0 at t=0 or t=-2since negative time has no physical significance, therefore t=0
Given- v=2t2e-ta=dv/dt =0= 2e-t (dt2/dt) + 2t2 (de-t/dt)0= 4t e-t +2t2[ {de-t/d(-t)}×{d(-t)/dt }]0= 4te-t - 2t2e-t0= 2te-t (2-t)Either 2te-t=0t=0Or 2-t =0t=2 So t =0 or t=2
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