n an auto accident, a car hit a pedestrian and the driver then slammed on the brakes to stop the car. During the subsequent trial, the driver's lawyer claimed that the driver was obeying the posted 35.0 mph speed limit, but that the limit was too high to enable him to see and react to the pedestrian in time. You have been called as the state's expert witness. In your investigation of the accident site, you make the following measurements: The skid marks made while the brakes were applied were 325 ft long, and the tread on the tires produced a coefficient of kinetic friction of 0.300 with the road.
If the driver's speeding ticket is $10 for each mile per hour he was driving above the posted speed limit, would he have to pay a ticket, and if so, how much would it be?
To determine whether the driver was speeding and, if so, by how much, we need to calculate the initial speed of the car before the brakes were applied. We can then compare this speed to the posted speed limit.
First, let's calculate the deceleration of the car using the skid marks and the coefficient of kinetic friction. The formula for calculating deceleration is:
deceleration = (coefficient of kinetic friction) x (acceleration due to gravity)
The acceleration due to gravity is approximately 32.2 ft/s^2.
plugging in the values:
deceleration = 0.300 x 32.2 ft/s^2
deceleration = 9.66 ft/s^2
Next, we need to determine the time it took for the car to come to a stop after the brakes were applied. We can use the equation:
final velocity = initial velocity + (acceleration x time)
Since the car came to a stop, the final velocity is 0. The initial velocity is what we need to find, and the acceleration is the deceleration we calculated earlier.
0 = initial velocity + (9.66 ft/s^2 x time)
Now, we can calculate the time it took for the car to come to a stop using the equation:
time = final velocity / (acceleration)
Since the final velocity is 0, the equation becomes:
time = 0 / (9.66 ft/s^2)
This indicates that the car took an infinitesimally small amount of time to come to a stop (instantaneous stop).
Now that we have the deceleration and time, we can calculate the initial velocity (speed) using the equation:
final velocity = initial velocity + (acceleration x time)
Since the final velocity is 0, the equation becomes:
0 = initial velocity + (9.66 ft/s^2 x 0)
This indicates that the initial velocity was 0 ft/s (the car was already stopped).
Based on these calculations, it is evident that the car was not speeding, as the initial velocity was 0 ft/s. Therefore, the driver would not have to pay a ticket for speeding.
However, it is worth noting that the driver's lawyer argued that the posted speed limit was too high for the driver to see and react to the pedestrian in time. While this argument may impact the driver's liability in the trial, it does not affect whether the driver was speeding or not.