A car is traveling at 55.1 km/h on a flat

highway.
The acceleration of gravity is 9.81 m/s
2. a) If the coefficient of kinetic friction between the road and the tires on a rainy day is
0.116, what is the minimum distance needed
for the car to stop

b) What is the stopping distance when the
surface is dry and the coefficient of kinetic
friction is 0.698

First of all, convert 55.1 km/h to 15.3 m/s

2a) The stopping distance X is given by this equation that relates the kinital kinetic energy to the work done against friction:
(1/2)M V^2 = M*g*Uk*X
Notice that the mass M cancels out, which is good since they did not tell you the mass.

X = V^2/(2*g*Uk) = 103 m

2b) Use the same formula, but with the different value of Uk (the kinetic friction corefficient). The stopping distance is much less.

To calculate the minimum distance needed for the car to stop, we need to consider the forces acting on the car.

a) When the road is wet and the coefficient of kinetic friction is 0.116:
The force of kinetic friction can be calculated using the equation:

Frictional force = coefficient of kinetic friction x normal force

The normal force is equal to the weight of the car, which can be calculated using the equation:

Normal force = mass x acceleration due to gravity

The deceleration of the car can be calculated using the equation:

Deceleration = frictional force / mass

Then, using the equation of motion:

Final velocity² = Initial velocity² + 2 x acceleration x distance

Since the car needs to come to a complete stop, the final velocity will be zero. We can rearrange the equation to solve for the distance:

Distance = (Final velocity² - Initial velocity²) / (2 x acceleration)

Substituting the given values into these equations will give us the minimum distance needed for the car to stop.

b) When the surface is dry and the coefficient of kinetic friction is 0.698:
The calculation process is similar to part a), but we will use the new coefficient of kinetic friction (0.698) instead. By following the same steps as above, we can find the stopping distance for the car on a dry surface.

Remember to convert the units to ensure they are consistent throughout the calculations.