# Minimum distance in which the car will stop?

• hm8
In summary, The car will stop in a minimum distance of 112.5 feet if the coefficient of static friction between the road and tires is 0.100. The mass of the car is not needed to solve the problem, and conservation of energy can also be used to solve it.
hm8

## Homework Statement

A car is traveling at 51.0 mi/h on a horizontal highway.
If the coefficient of static friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop?

## Homework Equations

$$\Sigma \vec{F} = m \vec{a}$$

$$v^2 = v_0^2 + 2 a \Delta x$$

$$f_s \leq \mu_s N$$

## The Attempt at a Solution

Is it possible to do this problem without mass? Or did my teacher just forget to give us the mass?

If I had the mass of the car, I'd use it to find the normal force, and then plug that into the friction equation to find the force of friction...and then plug that into Newtons 2nd to find acceleration, and then use kinematics to find distance.

I suppose the minimum distance would be 0 if the car's mass was infinite but...I don't think that's what he's looking for.

masses should drop out at the very end. Are you allowed to use conservation of energy? If you can than its just as simple as knowing the work done by the road and brakes

## What is the minimum distance in which a car will stop?

The minimum distance in which a car will stop depends on various factors, including the speed of the car, the condition of the road, and the type and quality of the car's brakes. It is generally recommended to maintain a safe following distance of at least 3-4 seconds from the car in front of you to allow for enough stopping distance.

## How does speed affect the minimum stopping distance of a car?

The higher the speed of a car, the longer the minimum stopping distance will be. This is because the car will have more momentum and will require more time and distance to come to a complete stop. It is important to always follow the speed limit and adjust your speed according to road and weather conditions to ensure a safe stopping distance.

## Can the condition of the road affect the minimum stopping distance of a car?

Yes, the condition of the road can significantly affect the minimum stopping distance of a car. Wet, icy, or uneven roads can decrease the friction between the tires and the road, making it more difficult for the car to stop quickly. It is important to drive cautiously and maintain a safe speed on roads with poor conditions.

## Do different types of brakes affect the minimum stopping distance of a car?

Yes, different types of brakes can affect the minimum stopping distance of a car. Cars with anti-lock braking systems (ABS) are able to stop in a shorter distance compared to cars with standard brakes. ABS prevent the wheels from locking up, allowing the driver to maintain control and stop more quickly. Regular maintenance of brakes is also important in ensuring they are functioning properly and able to stop the car effectively.

## What other factors can affect the minimum stopping distance of a car?

In addition to speed, road conditions, and brake type, the weight and condition of the car, as well as the driver's reaction time, can also affect the minimum stopping distance. Heavier cars require more force to stop, and if the driver is distracted or takes longer to react, it can lead to a longer stopping distance. It is important to always stay alert and focused while driving to minimize the risk of accidents.

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