Question

In the aftermath of a car accident, it is concluded that one driver slowed to a halt in 20 seconds while skidding 1775 feet. If the speed limit was 60 miles per hour, can it be proved that the driver had been speeding?

Answer 1

Assume uniformly accelerated motion

Vf = Vo - at => a= [Vo - Vf] / t

Vf = 0, t = 20 s => a = Vo / 20

x = Vot - at^2 / 2

x = Vot - (Vo / 20) * t^2 /2

x = 1775 feet * [1 mile / 5280 feet]  = 0.336 mile

t = 20 s

=> 0.336 = 20Vo - Vo(20)^2 /(40) = 20Vo - 10 Vo = 10 Vo

=> Vo = 0.336 /10  = 0.0336 mile /s

Vo = 0.0336 mile/s * 3600 s/h = 120.96 mile / h

Therefore, the car was way over the speed limit.