A particle moves along the parabolic path x=y2+2y+2 in such a way that the y-component of velocity vector remains 5m/s during the motion. The magnitude of acceleration of the particle is:

{x = y² + 2y + 2} is the constraint equation of motion of the particle, where x and y are time dependent coordinates. Hence we can differentiate the eq w.r.t time, and obtainẊ = 2yẏ + 2ẏ + 0 where ẋ (dot notation)implies dx/dt.̇Since ẏ = 5m/sẊ = 10y +10Again diff. w.r.t timeẍ = 10ẏ = 50m/sAs y component of velocityis constant, y component of accl. is nil, which gives us the final answera = 50i + 0j = 50m/s^2