Final answer:
The initial speed of the car can be estimated using the formula for kinetic energy and friction work. By inserting the given coefficient of friction (0.500) and the length of the skid marks (90.0 m) into the formula, we calculate the initial speed to be approximately 29.73 m/s.
Step-by-step explanation:
To estimate the speed of the car when the brakes were applied given the length of the skid marks and the coefficient of friction, we use the physics of motion and friction. We'll apply the formula for kinetic energy and work done by friction: the work done by friction is equal to the initial kinetic energy of the car.
The work done by the friction force is given by Work = friction force × distance, where the friction force is the coefficient
of friction × normal force. Because the car is on a flat road, the normal force is equivalent to the weight of the car, which is the mass of the car times the acceleration due to gravity (9.81 m/s²).
The initial kinetic energy of the car is given by Kinetic Energy = 1/2 × mass × velocity².
Assuming that the car comes to a stop, the work done by friction is equal to the car's initial kinetic energy.
Since the mass of the car cancels out from both sides, we are left with velocity² = 2 × coefficient of friction × acceleration due to gravity × distance of skid marks.
Solving for velocity gives us the initial speed of the car.
Plugging in the values from the question (coefficient of friction = 0.500 and skid mark length = 90.0 m), we can calculate the estimated speed.
Example calculation:
Initial Speed = sqrt(2 × coefficient of friction × acceleration due to gravity × skid mark length)
Initial Speed = sqrt(2 × 0.500 × 9.81 m/s² × 90.0 m)
Initial Speed = sqrt(883.8)
Initial Speed = 29.73 m/s