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?

Question

Mathematics

Stevenson

Today, 04:33

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?

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Imani Solomon · 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.