Question

If a child ran into the road 65 to 70 feet ahead of your vehicle, what is the highest speed from which you could stop with good brakes before hitting him? 30 mph 50 mph 40 mph 20 mph

Answer 1

Given:
Stopping distance range is d = (65, 70) ft.

The stopping distance, d, obeys this formula.
d = v²/(2μg)
where
v = speed of the vehicle
μ = 0.8, coefficient of static friction under good road conditions
g =  acceleration due to gravity, 32.2 ft/s²

Therefore
v = √(2*0.8*32.2*d) = 7.178√d

Test d = 65 ft.
v = 7.178√(65) = 57.87 ft/s = (57.87/88)*60 = 39.5 mph

Test d = 70 ft.
v = 7.178√(70) = 60.05 ft/s = 40.9 mph

To be safe, the lower speed of 39.5 mph is preferred.

Answer: 40 mph