You are invited as an engineer expert to a court where a speed limit violation i

Question

You are invited as an engineer expert to a court where a speed limit violation incident is considered. The car was traveling at an unknown speed V when a traffic policeman signaled the driver to stop. The driver pressed the brake pedal, thereby locking the wheels and forcing the car into a pure sliding motion until it stopped completely. The duration T of this sliding motion and the corresponding sliding length S are known: T = 4 sec and S = 40 meters. The driver argues that the ratio S/T is well within the permitted speed limit 30 miles per hour. Can you use the available data to estimate the actual value of V for the court

Explanation / Answer

S/T = 40/4=10 m/s

10 m/s = 36000 m/hr = 36000/1000 km/hr = 36 km/hr = 36*5/8 mph = 22.5 mph

so it appears his argument has some merit (numerically).

However this value represents the average speed over the stopping distance but the initial speed will be twice this value i.e. 45 mph.

v=u+at
0=45+a4
a=-45/4=-11.25 mph per hr deceleration

For deceleration F=ma or f*R=ma where f is the kinetic friction constant

R=m*g

So, f*m*g=m*a
f*g=a
f=a/g

a=-11.25 mph per hr = -11.25*88/60 ft/sec/hr = -11.25*88/60/60 ft/sec^2 = -0.275 ft/sec^2

f=-0.275/9.81 = -0.028

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