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DISCUSSION:

As you know, the velocity of P is tangent to the path (where the path here is the coaster track), whereas the acceleration has components both tangent and normal to the path:

v = ve_t
a = v_dot e_t + (v^2/rho) e_n

You are provided equations for v, rho and theta in terms of the distance s traveled along the path. Therefore, you can simply substitute those expressions into the above equations for the velocity and acceleration vectors. The only remaining task is to find the rate of change of speed, v_dot. Since the speed v is given not as a function of time, but instead as a function of s, we need to use the chain rule of derivatives to find v_dot; that is:

v_dot = dv/dt = (dv/ds)*(ds/dt) = v*(dv/ds)