Question

A car skids to a stop, leaving four skid marks with an average length of 60 feet. The road is asphalt. Skid tests reveal a drag factor of 0.75. Since all four wheels were braking, the braking efficiency is 100% or 1.00. To the nearest mile per hour, what was the car’s speed at the time of the accident.

Answer 1

37 mph

Explanation:

Sum of forces on the car in the y direction:

∑F = ma

N − mg = 0

N = mg

Sum of forces on the car in the x direction:

∑F = ma

-Nμ = ma

-mgμ = ma

-gμ = a

Given μ = 0.75 and g = 32 ft/s²:

a = -(32 ft/s²) (0.75)

a = -24 ft/s²

Use kinematics to find the initial velocity.

v² = v₀² + 2aΔx

(0 ft/s)² = v₀² + 2 (-24 ft/s²) (60 ft)

v₀ ≈ 53.7 ft/s

v₀ ≈ 37 mph