## Accelerating along a Racetrack

**A road race is taking place along the track shown in the figure . All of the cars are moving at constant speeds. The car at point F is traveling along a straight section of the track, whereas all the other cars are moving along curved segments of the track.**

**A) ****Let be the velocity of the car at point A. What can you say about the acceleration of the car at that point?**

**B) Let be the velocity of the car at point C. What can you say about the acceleration of the car at that point?**

**C) Let be the velocity of the car at point D. What can you say about the acceleration of the car at that point?**

**D)** **Let be the velocity of the car at point F. What can you say about the acceleration of the car at that point?**

**E)**** Assuming that all cars have equal speeds, which car has the acceleration of the greatest magnitude, and which one has the acceleration of the least magnitude?**

**F) Assume that the car at point A and the one at point E are traveling along circular paths that have the same radius. If the car at point A now moves twice as fast as the car at point E, how is the magnitude of its acceleration related to that of car E.**

## Answer ( 1 )

A)Let be the velocity of the car at point A. What can you say about the acceleration of the car at that point?=> The acceleration is perpendicular to

and directed toward the inside of the track.B) Let be the velocity of the car at point C. What can you say about the acceleration of the car at that point?=> The acceleration is perpendicular to

and pointed toward the inside of the track.C) Let be the velocity of the car at point D. What can you say about the acceleration of the car at that point?=>The acceleration is perpendicular toand pointed toward the outside of the track.D)Let be the velocity of the car at point F. What can you say about the acceleration of the car at that point?=>The acceleration is zero.E)Assuming that all cars have equal speeds, which car has the acceleration of the greatest magnitude, and which one has the acceleration of the least magnitude?Use A for the car at point A, B for the car at point B, and so on. Express your answer as the name the car that has the greatest magnitude of acceleration followed by the car with the least magnitude of accelation, and separate your answers with a comma.=> D,FF) Assume that the car at point A and the one at point E are traveling along circular paths that have the same radius. If the car at point A now moves twice as fast as the car at point E, how is the magnitude of its acceleration related to that of car E.=> The magnitude of the acceleration of the car at point A is four times that of the car at point E.