The coefficiant of friction between rubber tires and wet pavement is 0.5, and the breaks are applied to 750kg car, intitally travelling at 30m/s and the car skids to a stop. What is size and difection of the acceleration. How do i find acceleration of the vehicle

To find the acceleration of the vehicle, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on the object divided by its mass. In this case, the net force can be determined by considering the forces involved.

First, let's calculate the force of friction between the tires and the wet pavement. The frictional force can be determined using the formula:

Frictional force = coefficient of friction * Normal force

The normal force is the force exerted on the car by the pavement, which is equal to the weight of the car (mass * gravitational acceleration).

Given:
Coefficient of friction (μ) = 0.5
Mass of the car (m) = 750 kg
Initial velocity (u) = 30 m/s
Final velocity (v) = 0 m/s

Using the equation of motion:
v^2 = u^2 + 2as

Since the car comes to a stop, v = 0, and the equation simplifies to:
0 = (30^2) + 2a * s

Solving for acceleration (a):
a = (-30^2) / (2 * s)

Rearranging the equation gives:
s = (-30^2) / (2 * a)

Now, we can find the distance (s) covered during the skid. Rearranging the equation gives you the equation for distance:

s = (-30^2) / (2 * a)

Next, we can substitute this value of s into the equation for the frictional force:
Frictional force = (0.5) * (mass * gravitational acceleration)

Finally, we can use Newton's second law to find the acceleration:
Net force = Frictional force
Net force = mass * acceleration

Therefore:
mass * acceleration = (0.5) * (mass * gravitational acceleration)

Simplifying the equation:
acceleration = 0.5 * gravitational acceleration

The direction of the acceleration is opposite to the direction of motion, so it is negative.

Therefore, the size of the acceleration is 0.5 times the gravitational acceleration, and the direction is negative.