The coordinates of a moving particle at any time ‘t’ are given by x=αt3 and y=βt3 . The speed of the particle at time ‘t’ is given by

given coordinate of moving particle→x=αt3 differentiate w.r.t. time,  to get velocity ⇒velocity x component=Vx=dxdt ⇔Vx=dαt3dt ⇒Vx=α3t2 given coordinate of moving particle→y=βt3 differentiate w.r.t. time,  to get velocity ⇒velocity y component=Vy=dydt ⇒Vy=dβt3dt ⇒Vy=β3t2  At a time ‘t’ the speed of the particle is V=vx2+vy2 substitute obtained values, ⇒V=α3t22+β3t22 ⇒V=α29t4+β29t4 ⇒V=3t2α2+β2=speed of the particle at time t