The motion of a particle along a straight line is described by equation : x = 8 +12t -t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

v = dxdt = 12-3t2     ---(i)If velocity is zero, 12-3t2 = 0 which gives t = 2 secFor acceleration again differential equation (i)a = d2xdt2  = -6t----(ii)At time t = 2 sec, a = -6×2 = -12 m/s2Hence retardation = 12 m/s2