Final answer:
The distance the tires skid on the road can be calculated by finding the acceleration of the car using the equation of motion and the force of friction. The tires skid for approximately 65.57 feet on the road.
Step-by-step explanation:
To determine the distance the tires skid on the road, we need to calculate the acceleration of the car. We can use the equation of motion:
v^2 = u^2 + 2as
where v is the final velocity (0 ft/s), u is the initial velocity (20 ft/s), a is the acceleration, and s is the distance traveled.
Since the driver jams on the brakes, the force of friction will cause the car to decelerate. The force of friction can be calculated using the equation:
f_friction = mu_k * m * g
where f_friction is the force of friction, mu_k is the coefficient of kinetic friction (0.5), m is the mass of the car (3500 lb), and g is the acceleration due to gravity (32.2 ft/s^2).
Using the force of friction, we can calculate the acceleration using Newton's second law:
f_friction = m * a
Now we can substitute the known values and solve for the acceleration:
a = f_friction / m = (mu_k * m * g) / m = mu_k * g
Finally, we can substitute the values for acceleration and initial velocity into the equation of motion to find the distance traveled:
0^2 = (20 ft/s)^2 + 2 * a * s
Simplifying the equation:
s = -(20 ft/s)^2 / (2 * a) = -200 ft^2 / a
Substituting the value for acceleration, we can calculate the distance traveled:
s = -200 ft^2 / (mu_k * g)
Therefore, the tires skid for approximately 65.57 feet on the road.