Final answer:
The calculation using the given coefficient of friction and skid mark length suggests that the initial speed was about 14.8 m/s, which is above the speed limit of 13.4 m/s. Therefore, it would likely not be beneficial to fight the speeding ticket in court based solely on this information.
Step-by-step explanation:
To determine if you should fight the speeding ticket in court, we need to calculate the initial speed of the car before the brakes were applied using the length of the skid mark and the coefficient of friction. The formula to find the stopping distance when the final velocity is zero (the car came to a stop) is derived from the work-energy principle and is given as:
distance = (initial velocity)^2 / (2 × coefficient of friction × g)
where g is the acceleration due to gravity (9.8 m/s²). Rearranging the formula to solve for initial velocity gives us:
initial velocity = sqrt(2 × coefficient of friction × g × distance)
Plugging in the numbers:
initial velocity = sqrt(2 × 0.55 × 9.8 m/s² × 30.5 m)
When you calculate this, you get an initial velocity of approximately 14.8 m/s.
Since the initial velocity exceeds the speed limit of 13.4 m/s (30 mph), it suggests you were indeed speeding, and thus it would likely not be beneficial to fight the ticket in court based on this calculation. However, you might consider other factors, such as accuracy of the measurement of the skid mark or coefficient of friction, before making a final decision.