The displacement of particle varies with time as x=at2−bt3. Then find the displacement  of the particle when  its acceleration is zero

x=at2−bt3  at t=0⇒x=0to find velocity, differentiate x with respect to time Velocity =V=dxdt=2at−3bt2to find acceleration, differentiate again x with respect to time Acceleration= a=dvdt=2a−6bt If a=0 2a−6bt=0⇒t=a3b=time The position at, time t=a3bx=at2−bt3⇒x=aa3b2−ba3b3⇒x=a39b2−a327b2=2a327b2 Displacement S=2a327b2−0⇒S=2a327b2