The centripetal acceleration of the car following a curve with a radius of 500 m at a speed of 25.0 m/s is 1.25 m/s^2. It is much smaller than the acceleration due to gravity for this fairly gentle curve taken at highway speed.
The centripetal acceleration of a car following a curve can be calculated using the formula:
a = v^2 / r
where a is the centripetal acceleration, v is the velocity of the car, and r is the radius of the curve.
For the given values:
v = 25.0 m/s
r = 500 m
Substituting the values into the formula, we get:
a = (25.0^2) / 500 = 1.25 m/s^2
The acceleration due to gravity is approximately 9.8 m/s^2.
Since the centripetal acceleration is much smaller (1.25 m/s^2), it can be considered negligible compared to the acceleration due to gravity for this fairly gentle curve taken at highway speed.