The position x of a particle varies with time t as  x=at2−bt3. The acceleration of the particle will be zero at time t equal to

given  Position of particle  x=at2−bt3differentiate w.r.t. time t to get velocity velocity =dxdt=dat2−bt3dt⇒v=2at−3bt2again differentiate w.r.t. time t to get acceleration Acceleration =dvdta=d2at−3bt2dt⇒2a−6bt Acceleration will become zero O=2a−6bt⇒2a=6bt⇒t=a3b=time in which acceleration becomes zero