Rubber tires and wet blacktop have a coefficient of kinetic friction of 0.5. A pickup truck with a mass 750 kg traveling 30.0 m/s skids to a stop. (a) what is the size and direction of the frictional force that the road exerts on the truck? (b) Find the acceleration of the truck. (c) How far would the truck travel before coming to rest?

To answer these questions, we need to apply the principles of Newton's laws of motion and the equations of motion. Here's how we can solve each part:

(a) To find the size and direction of the frictional force, we need to use the equation:

Frictional force = coefficient of kinetic friction * normal force

The normal force is the force exerted by the road on the truck perpendicular to the surface. In this case, it is equal to the weight of the truck, which can be calculated as:

Normal force = mass * gravity

where gravity is approximately 9.8 m/s².

Substituting the given values:

Normal force = 750 kg * 9.8 m/s² = 7350 N

Now, we can calculate the frictional force:

Frictional force = 0.5 * 7350 N = 3675 N

The frictional force acts in the opposite direction to the motion of the truck, so it is in the negative direction.

Therefore, the size of the frictional force is 3675 N, and its direction is opposite to the truck's motion.

(b) To find the acceleration of the truck, we can use the equation:

Force = mass * acceleration

In this case, the net force acting on the truck is the frictional force, so:

Frictional force = mass * acceleration

Rearranging the equation, we can solve for the acceleration:

Acceleration = Frictional force / mass

Acceleration = 3675 N / 750 kg

Acceleration ≈ 4.9 m/s²

Therefore, the acceleration of the truck is approximately 4.9 m/s².

(c) To calculate the distance traveled by the truck before coming to a stop, we can use the equation of motion:

v² = u² + 2as

where:
- v is the final velocity (0 m/s, as the truck comes to a stop)
- u is the initial velocity (30.0 m/s)
- a is the acceleration (from part b, 4.9 m/s²)
- s is the distance traveled

Rearranging the equation, we can solve for the distance traveled:

s = (v² - u²) / (2a)

Substituting the values:

s = (0 m/s)² - (30.0 m/s)² / (2 * 4.9 m/s²)

s = -900 m²/s² / 9.8 m/s²

s ≈ -92.1 m

Since distance cannot be negative, the truck traveled approximately 92.1 meters before coming to a stop.

Note: The negative sign indicates the opposite direction of the initial motion.

Therefore, the truck would travel approximately 92.1 meters before coming to rest.