a particle move along the parabolic path x=ysquare+2y+2 in such a way that the y component of velocity vector remains 5 m/s during the motion. the magnitude of the acceleration is?

x = y² + 2y +2

 

differentiating the equation with respect to time

 

thus dx/dt = 2y dy/dt + 2dy/dt

or Vx = 2y Vy + 2 Vy

 

here Vy = 5 m/s a constant

 

now Vx = 10y + 10

differentiating again with time:

d²x/dt² = a = 10 dy/dt = 10 Vy = 50 m/s²