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?
1 answer:
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.
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