Acar is traveling at 52.0 mi/h on a horizontal highway. (a) if the coefficient of static friction between road and tires on a rainy day is 0.102, what is the minimum distance in which the car will stop? m (b) what is the stopping distance when the surface is dry and µs = 0.603? m

First of all, let's convert the initial speed from mi/h to m/s.
We know that 1 mi=1609 m and 1 h=3600 s. So, the conversion factor is:

And the initial speed of the car is therefore:

Now we can start to solve the problem.

a) I assume that 0.102 is the coefficient of dynamic friction, not static friction, because the car is in motion.
The only force acting on the car is the frictional force, directed against the motion of the car. We can write Newton's second law for the car:

where m is the mass of the car, a its acceleration, and is the frictional force, with a negative sign since it is acting against the motion of the car. Simplifying m and solving, we can find the acceleration of the car:

The acceleration is negative because the car is decelerating.

Now we can use the following relationship valid for a uniformly accelerated motion:

where S is the distance covered, vi and vf are the initial and final speed of the car. Since the car is going to stop, , and by replacing a and viwith the values we calculated previously, we can find the distance S that the car needs to stop:


b) The procedure to solve this part of the exercise is exactly identical to the first part, the only difference is the value of the coefficient of friction: . Let's start by calculating the new acceleration

And then, the new distance needed to stop the car is

So, when the surface is dry the car needs much less space to stop completely than when the surface is wet.

So what is the question

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.