A rollercoaster car starts at rest on top of a frictionless hill of height 17 m, slides down to ground level, and then into a frictionless loop of radius 5 m.

Question

When the car is at the side of the loop (level with the center), find the magnitude of the car's tangential acceleration:

Answer 1

It fell a distance of 12 m, so it has that energy as velocity.

mg(h)=1/2 mv^2
mg dh/dt= m dv/dt

g dh/dt= dv/dt

now dv/dt is tangential acceleration.
dh/dt is tangential velocity. You can get velocity from
1/2 mv^2=mgh for h=12