A roller coaster has a mass of 585 kg when fully loaded with passengers. A)If the vehicle has a speed of 18.0 m/s at point a, what is the force (in N) of the track on the vehicle at this point?
B) What is the maximum speed (in m/s) the vehicle can have at point B in order for gravity to hold it on the track?
Point A says the radius is 10m. Point B says radius is 15m.

Explanation:

I'm going to ASSUME that point A is at the bottom of a circular curve.

The track must support the weight of the car and also supply the needed centripetal force

F = mg + mv²/R

F = 585(9.81 + 18.0²/10) = 24,692.85

F = 24.7 kN

I'm going to ASSUME that point B is at the top of a circular curve.

The track must support the weight of the car and also supply the needed centripetal force.

At a minimum, the weight can be reduced to zero and all the gravity acceleration acts as centripetal acceleration.

0 = mg - mv²/R

        g = v²/R

         v = √Rg = √(15(9.81) = 12.1305399...

        v = 12.1 m/s

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)