After t seconds, the acceleration of a particle, which starts from rest and moves in a straight line is (8- t 5 ) cm / s ^2 , then velocity of the particle at the instant, when the acceleration is zero, is

Step-by-step solution

Acceleration = (8- t 5 ) cm / s ^2 dv dt =8- t 5 Integrating on both sides, we get v=8 t- t^2 10 +c...(i) At t=0, v=0 array ll & 0=8(0)-0+c c=0 & v=8 t- t^2 10 ...ii[From(i)] array Acceleration =0 aligned & dv dt =0 & 8- t 5 =0 & t =40 aligned Substituting t =40 in (ii), we get Velocity (v)=8(40)- (40)^2 10 =160 ~cm / s