Final answer:
The car was traveling at a speed of 25.44 m/s before skidding to a halt on the wet road with a kinetic coefficient of friction of 0.50. This was calculated by equating the work done by friction to the initial kinetic energy of the car.
Step-by-step explanation:
To determine how fast a 1500 kg car was traveling when it leaves 66-meter-long skid marks on a wet road with a kinetic coefficient of friction (μk) of 0.50, we can use the work-energy principle. The work done by friction is equal to the kinetic energy the car had before coming to a stop. The work done by friction (W) can be calculated using the formula W = μk * m * g * d, where m is the mass of the car, g is the acceleration due to gravity (9.81 m/s2), and d is the distance of the skid marks. The initial kinetic energy (KEi) of the car is given by the formula KEi = ½ * m * v2, where v is the initial velocity of the car we are solving for.
By setting the work done by friction equal to the initial kinetic energy, we get μk * m * g * d = ½ * m * v2. Simplifying this, we can solve for v: v = sqrt(2 * μk * g * d). Plugging in the values, we find the initial velocity v = sqrt(2 * 0.50 * 9.81 m/s2 * 66 m) = sqrt(647.4) m/s = 25.44 m/s.
Therefore, the car was traveling at a speed of 25.44 m/s before it skid to a halt on the wet road.