Question

A particle moves with constant speed of 3m/sec along path y=3x^2
What is the acceleration of the particle at x=1.5m?

Answer 1

Since the speed is constant, the acceleration must be caused by the change in direction. The angle of the trajectory to the x axis is
theta = arctan (dy/dx) = arctan (6x)
When x = 1.5, theta = arctan 9 = 83.66 degrees
The acceleration will be
(speed)x d(theta)/dt
= (speed)* d(theta)/dx* dx/dt

Take it from there.