You are driving a 2520.0 kg car at a constant speed of 14.0 m/s along an icy, but straight, level road. As you approach an intersection, the traffic light turns red. You slam on the brakes. Your wheels lock, the tires begin skidding, and the car slides to a halt in a distance of 25.5 m. What is the coefficient of kinetic friction between your tires and the icy road?

vf^2=vi^2 + 2ad

solve for a. Then note that a=mu*g

To find the coefficient of kinetic friction between the tires and the icy road, we need to use the concepts of force, friction, and the motion of the car.

First, let's determine the net force acting on the car. In this case, the only force acting on the car is the force of kinetic friction opposing the motion. When the wheels lock and the tires begin skidding, the force of kinetic friction is responsible for slowing down the car.

The force of kinetic friction is given by the equation:

F_friction = μ_k * N

where μ_k is the coefficient of kinetic friction and N is the normal force between the car's tires and the road. Since the car is on a level road and moving at a constant speed, the normal force is equal to the car's weight.

Next, we need to calculate the normal force (N) acting on the car. The normal force is the force exerted by the road perpendicular to the car's weight. In this case, since the car is on a level road, the normal force is equal to the car's weight (mg), where m is the mass of the car and g is the acceleration due to gravity (9.8 m/s^2).

N = mg

Now, let's calculate the net force acting on the car. The net force can be calculated using Newton's second law:

Net Force = mass * acceleration

Since the car comes to a halt, the final velocity is 0 m/s, and the initial velocity is 14.0 m/s (given). The distance covered by the car during braking is 25.5 m (given).

Using the formula:

(v^2 - u^2) = 2as

where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance covered, we can solve for the acceleration (a):

(0^2 - 14^2) = 2 * a * 25.5

Rearranging the equation:

a = (0 - 196) / (2 * 25.5)

Calculating the value of acceleration (a):

a = -196 / 51

Now, plug in the values obtained into Newton's second law equation:

Net Force = mass * acceleration
F_friction = μ_k * N
μ_k * m * g = m * a

Cancelling out the mass (m) from both sides of the equation, we get:

μ_k * g = a

Substituting the value of acceleration (a) calculated earlier:

μ_k * g = -196 / 51

Finally, solve the equation for the coefficient of kinetic friction (μ_k):

μ_k = (-196 / 51) / g

Substituting the value of g (acceleration due to gravity):

μ_k = (-196 / 51) / 9.8

Calculating the value:

μ_k ≈ -0.392

The coefficient of kinetic friction between the tires and the icy road is approximately -0.392. Note that the negative sign indicates that the force of kinetic friction is acting in the opposite direction to the car's motion.