Question

A 745i BMW car can brake to a stop in a distance of 122 ft from a speed of 60.0 mi/h. To brake to a stop from a speed of 80.0 mi/h requires a stopping distance of 221 ft. What is the average braking acceleration for the following intervals? Express the answers in mi/h/s and in m/s^2

60 mi/h to rest, 80 mi/h to rest,80 mi/h to 60 mi/h

Answer 1

Vf^2 = Vo^2 + 2ad
0 = Vo^2 + 2ad
Vo^2 = -2ad
At 60 mph:
V^2 = -2ad => a = -V^2/2d
a = (60.0 mi/h)^2 / (2)(0.0231mi)
a = -77901.64 mi/h^2
1 mi/h^2 = 3600 mi/(h*s) (why?)
1 mi/(h*s) = 1609m/(3600s)(1s) = 0.447 m/s^2
a = -21.64 mi/h/s = -9.67 m/s^2
You calculate the acceleration when Vo = 80 mph in a similar fashion.