A particle starts from the origin of coordinates at time t = 0 and moves in the x - y plane with a constant acceleration α in the y -diretion. Its equation of motion is y = β x 2 . Its velocity component in the x -direction is

Step-by-step solution

Equation of motion is y = β x 2 d 2 y dt 2 = α d 2 x dt 2 = 0 from y = x dy dt = 2 x dx dt β d 2 y dt 2 = 2 dx dt 2 + 2x d 2 x dt 2 β a y = 2 dx dt 2 + 0 β a y = 2 v x 2 β v x = a y 2 β = α 2 β