Final answer:
The magnitude of the car's total acceleration, which is the centripetal acceleration, is calculated to be 9.0 m/s², using the formula a_c = v² / r.
Step-by-step explanation:
The question pertains to finding the magnitude of the car's total acceleration as it travels with a constant tangential speed of 75.0 m/s around a circular track of radius 625 m. The only acceleration the car would experience in such a case is centripetal acceleration, which keeps the car moving in a circular path.
To calculate the centripetal acceleration (ac), we use the formula:
ac = v2 / r
where v is the tangential speed and r is the radius of the circular path.
Substituting the values given, we get:
ac = (75.0 m/s)2 / 625 m = 9.0 m/s2
The magnitude of the car's total acceleration, which is the same as its centripetal acceleration in this case, is 9.0 m/s2.