Distance needed for the car to stop

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In summary: So, the car will stop when the distance it travels is less than the value calculated with the given coefficient of friction.
  • #1
lovelylemon
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"A car is traveling at 70.4 m/h on a horizontal highway. The acceleration of gravity is 9.8 m/s^2. If the coefficient between the road and tires on a rainy day is 0.052, what is the minimum distance in which the car will stop?"

I can't figure out how to solve this problem. To find the frictional force, I need the normal force, and to find the normal force I need the mass right?
 
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  • #2
lovelylemon said:
"A car is traveling at 70.4 m/h on a horizontal highway. The acceleration of gravity is 9.8 m/s^2. If the coefficient between the road and tires on a rainy day is 0.052, what is the minimum distance in which the car will stop?"

I can't figure out how to solve this problem. To find the frictional force, I need the normal force, and to find the normal force I need the mass right?

is the car traveling in meters per hour or miles per hour. your unit notation is ambiguous. but anyway. with the information give, you either have to derive the information from the information you have, in which case you would need to figure out how the coefficient of friction was calculated which should give you the cars mass, or mass will not play a part in this because you have been given all the information you need to calculate the unknowns.
 
  • #3
lovelylemon said:
"A car is traveling at 70.4 m/h on a horizontal highway. The acceleration of gravity is 9.8 m/s^2. If the coefficient between the road and tires on a rainy day is 0.052, what is the minimum distance in which the car will stop?"

I can't figure out how to solve this problem. To find the frictional force, I need the normal force, and to find the normal force I need the mass right?

In this case, where the force is parallel (actually anti-parallel, but taking just the magnitude you can ignore this) to the distance travelled, work is defined as force times distance. And by the work energy theorem, work is also defined as the change in kinetic energy; kinetic energy final minus kinetic energy initial. Set this equation up, remember that the force in the work equation is due to friction and you should be able to work it from there.
 

1. How does the speed of the car affect the distance needed to stop?

The higher the speed of the car, the longer the distance needed to stop. This is because the car has more momentum and takes longer to decelerate.

2. What other factors besides speed affect the distance needed to stop?

The weight of the car, the condition of the brakes, and the road surface also play a role in the distance needed to stop. Heavier cars and worn brakes require more distance to stop, while a rough or wet road surface can increase the stopping distance as well.

3. Is there a specific formula to calculate the distance needed to stop?

Yes, the formula is d = v2 / 2a, where d is the distance, v is the initial velocity, and a is the deceleration rate. However, this formula only works in ideal conditions and may vary in real-life situations.

4. How can I ensure I have enough distance to stop in an emergency?

It is recommended to keep a safe following distance from the car in front of you, at least 3 seconds in good weather conditions and more in adverse conditions. This will give you enough time to react and stop safely in case of an emergency.

5. Can I rely on the posted speed limit to determine the distance needed to stop?

No, the posted speed limit is just a general guideline and does not take into account variables such as road conditions, weather, and the weight of your car. It is always important to adjust your speed and following distance accordingly to ensure safe stopping in any situation.

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