Question

A freeway exit curves with a radius of 30 m and a posted speed limit of 17.5 m/s. What is your radial acceleration if you take this exit at the posted speed?

A. 7.3 m/s²
B. 3.5 m/s²
C. 1.3 m/s²
D. 10.2 m/s²

Answer 1

The radial acceleration of a car taking a freeway exit curve with a radius of 30 m at the posted speed limit of 17.5 m/s is calculated using the centripetal acceleration formula to be 10.2 m/s².

Step-by-step explanation:

To find the radial acceleration when the student takes the freeway exit at the posted speed limit, we use the formula for centripetal acceleration, which is a = v^2 / r, where v is the velocity and r is the radius of the curve.

Given the speed limit as 17.5 m/s and the radius of the curve as 30 m, we plug the values into the formula:

a = (17.5 m/s)^2 / 30 m

a = 306.25 m^2/s^2 / 30 m

a = 10.208 m/s^2

So, the radial acceleration of the car taking the exit at the posted speed is 10.2 m/s².