Physics problem - car accident?

An accident occurred when the driver of an automobile traveling down an 8% grade (slope) hit a parked car. A photograph of the accident scene revealed skid marks leading directly to the parked car. Fortunately, no one was injured by this rear end collision. The police officers responding to the call took a statement from the driver, measured the length of the skid marks, and performed a number of skid tests at the accident site. In their final report, the officers reported that the skid marks were 30 m long, that the coefficient of friction was 0.45, and that the driver recalled slamming on her breaks and sliding into the parked car. A footnote in the report indicates that the skid tests were performed over the first 6 m of the skid marks. You must decide, based on the evidence, whether the driver should be given a ticket for exceeding the 25 mph speed limit in the school zone where the accident occurred. If convicted, the driver will also receive 3 points against her driving record. Having already aculated 4 points against her record in previous violations, the driver immediately hires an investigator to challenge any incriminating evidence. The investigator arrives on the scene before the cars are towed. (a) ume that the car is a point m and draw a free body diagram showing all the forces acting on it as it slides down the hill. (b) The police made the umption that the coefficient of friction over the first 6 m was the same as that of the rest of the skid marks. Using this umption, calculate the acceleration of the car. (c) ume an initial velocity of 25 mph, how far would the car have traveled before stopping? (d) If the case goes to court, the judge would want to know the minimum velocity of the car before the driver applied the breaks. Calculate the minimum initial velocity of the car. (e) Based on the evidence in the accident report and the umptions used by the police, do you recommend to the police that the driver be charged with speeding?