A particle starts from rest and moves with acceleration a which varies with time t as  a=kt where k is a constant. The displacement  s of the particle at time  t is

Initial velocity,  u=0Acceleration a=kt (Where  k is constant)⇒dvdt=kt∵a=dvdt⇒∫0vdv=∫0tktdtIntegrating both sides, we get v=kt22∵v=dxdt⇒dxdt=kt22⇒∫0x dx=∫0t k2t2dtAgain integrating both sides, we get x=k6t3=16kt.t2∴x=16at2