A police man hears a car skidding as it comes to a halt at a traffic light.
He suspects that the car was going way over speed before it slammed on the
breaks. From knowledge of the tire-road surface interface he knows that
while it skidded the deceleration of the car was
4 m/2
. He measures the length of the skid mark to be 50 m. What was
the speed of the car when the skid mark started?
We can solve this the standard way by using formulae for x(t)
and v(t). The problem is that we will be forced to determine the time
it took to stop, something that we are not really interested in. To avoid this
we use formula 12 in which t has been suppressed. We have
The information given is that
here t is the exact time when the car came to a halt so that equation
is rather obvious. For the deceleration we have
Note the very important sign which indicates that the velocity
is decreasing rather than increasing. Putting in these numbers
we get immediately
Rather fast indeed for a traffic light zone!