The velocity of a particle at time t is given by the relation v=6 t - t ^2 6 . Its displacement S is zero at t =0 , then the distance travelled in 3 sec is

Step-by-step solution

v =6 t - t ^2 6 and we know that v = ds dt aligned & d s= (6 t - t ^2 6 ) dt & s = 6 t ^2 2 - t ^3 6(3) + c s =3 t ^2- t ^3 18 + c aligned We know that s =0 , when t =0 c =0 s =3 t ^2- t ^3 18 ( s )_ t =3 =3(3)^2- (3)^3 18 = 51 2 units