Asports car skids to a stop, leaving skid marks 290 m long.

if the coefficient of kinetic friction between tires and pavement is 0.80, how fast was the car going before the skid?

67.4 m/s

Explanation:

The force acting on the car, and that causes the car to slow down, is the force of friction, which is given by:

where

is the coefficient of kinetic friction

m is the mass of the car

is the acceleration of gravity

According to Newton's second law:

where F is the net force on the car and a its acceleration. Comparing the two equations, we find an expression for the acceleration:

(1)

Since the motion of the car is a uniformly accelerated motion, we can use the following equation:

where

v = 0 is the final velocity of the  car

u is the initial velocity

a is the acceleration

s = 290 m is the distance covered by the car while slowing down

Using (1) and solving for u, we find the initial velocity: