A 1.30×103 kg car skids to a halt on a wet road where μk = 0.600. How fast was the car travelling if it leaves a 65.0 m long skid? 19.5 m/s 27.6 m/s 5.88 m/s 0.767 m/s

To solve this problem, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

Step 1: Identify the forces acting on the car. The force of kinetic friction is the only force doing work on the car, and it acts in the opposite direction to the car's motion. The force of kinetic friction can be calculated using the equation F = μk * m * g, where μk is the coefficient of kinetic friction, m is the mass of the car, and g is the acceleration due to gravity (9.8 m/s²).

Step 2: Calculate the force of kinetic friction. F = μk * m * g = 0.600 * 1.30×10³ kg * 9.8 m/s² = 7620 N.

Step 3: Calculate the work done by the force of kinetic friction. The work done by a force is equal to the force times the distance over which it acts. In this case, the work done by the force of kinetic friction is W = F * d = 7620 N * 65.0 m = 495300 J.

Step 4: Set the work done by the force of kinetic friction equal to the change in the car's kinetic energy and solve for the car's initial speed. The car's initial kinetic energy was (1/2) * m * v², and its final kinetic energy was 0, because the car came to a stop. Therefore, we have the equation 495300 J = (1/2) * 1.30×10³ kg * v².

Step 5: Solve for v. v = sqrt((2 * 495300 J) / 1.30×10³ kg) = 27.6 m/s.

So, the car was initially traveling at a speed of 27.6 m/s.