# Stopping Distance with Vi and Coefficient of friction.

• kitenyos
In summary, if the coefficient of friction between road and tires on a rainy day is 0.13, the car will stop at a minimum distance of 1 mile.
kitenyos

## Homework Statement

A car is traveling at 66.9 mi/h on a horizontal highway.
The acceleration of gravity is 9.8 m/s2 .
If the coefficient of friction between road and tires on a rainy day is 0.13, what is the minimum distance in which the car will stop? (1 mi = 1.609)
Vi=29.9m/s
mu=.13
Vf=0m/s

Ff=(Fn)(mu)

## The Attempt at a Solution

There is no mass so i cannot calculate the normal force and i cannot calculate the Ff. At first I thought this problem was impossible because of lack of information but i did some research and all i could find is that "the mass cancels out". I do not understand this.

Write down the complete formulas without plugging in the numbers.
Then see you don't need the mass.

If you still can't get it, decide yourself a mass (eg. 1000kg) then try another mass to see if the result changes.

Which formulas? The Ff=(FN)(mu) ?

The complete formula/s !
Then what do you do with Ff ?

Well i plugged in 1000kg for mass and got 9800N for normal force so Ff=1274N. Not i need to figure out what to do with Ff. If the mass is 1000kg then it is raveling with a force of 29900N (F=MV). So there is 29900N forcer going forward and a 1275.3N Force of friction. I do not know what i do from here.

F=MV ?
Really ? Force = mass x velocity ?

No it doesn't i was wrong. F=mass x acceleration. Acceleration is 0 because it is a constant velocity. So wouldn't that mean that force=0 because 1000kg x 0= 0. So then wouldn't there only be force of friction?

Yes, and friction is slowly stopping the car. How long does it take ?

What is the formula for that. This is just a guess. T=A/Ff? So T=29900/1274? T=23.47s? And then i used the kinematics equation DeltaX= vf+vi/2 x t and got 350.88 m

Yes this is correct. Thank you very much!

## 1. What is stopping distance?

Stopping distance refers to the distance that a moving object, such as a car, travels after the brakes are applied until it comes to a complete stop.

## 2. How is stopping distance calculated?

Stopping distance can be calculated using the formula: stopping distance = initial velocity (Vi) * reaction time + (Vi^2 / 2 * coefficient of friction * acceleration due to gravity).

## 3. What is Vi?

Vi, also known as initial velocity, is the initial speed of a moving object before the brakes are applied. It is an important factor in calculating stopping distance.

## 4. What is coefficient of friction?

Coefficient of friction is a measure of the amount of friction between two surfaces. In the context of stopping distance, it is used to determine the force needed to bring a moving object to a stop.

## 5. How does the coefficient of friction affect stopping distance?

The higher the coefficient of friction, the greater the friction force between the tires and the road, resulting in a shorter stopping distance. On the other hand, a lower coefficient of friction will result in a longer stopping distance.

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