Stopping Dist. Car @100km/h on Flat Surface

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In summary, the minimal stopping distance for a car moving at an initial speed of 100km/h on a flat surface is 60m. When the car is moving down at 10 degrees, the stopping distance is 83.3m and when it is moving up at 10 degrees, the stopping distance is also 83.3m. The coefficient of friction for the flat surface is 0.657 and the acceleration of the car is -4.64m/s^2. The equation used to find the coefficient of friction is Uk = V^2 /(2gs). The mass of the car is not considered in the calculation of acceleration.
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inner08
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The minimal stopping distance for a car moving at an initial speed of module 100km/h is 60m on a flat surface. What is the stopping distance when the car is moving a) down at 10 degrees b) up at 10 degrees? We assume that the initial velocity and surface don't change.

I was thinking I could find the coefficient of friction of the flat surface (Uk = V^2/(2ag) which would give me Uk = 0.657. Then I would find the acceleration of the car by adding all the vectors together (mgsin(theta) - f = mA). The mass cancels out therefore giving me a = gsin(theta) - Ukgcos(theta) which in terms gives me a = -4.64. I then substitute the values in Vf^2 = Vi^2 + 2ad which gives me d = 83.3m. The answer to b would be mostly the same work switching up the sin/cos. Does that work?
 
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inner08 said:
The minimal stopping distance for a car moving at an initial speed of module 100km/h is 60m on a flat surface. What is the stopping distance when the car is moving a) down at 10 degrees b) up at 10 degrees? We assume that the initial velocity and surface don't change.

I was thinking I could find the coefficient of friction of the flat surface (Uk = V^2/(2ag) which would give me Uk = 0.657. Then I would find the acceleration of the car by adding all the vectors together (mgsin(theta) - f = mA). The mass cancels out therefore giving me a = gsin(theta) - Ukgcos(theta) which in terms gives me a = -4.64. I then substitute the values in Vf^2 = Vi^2 + 2ad which gives me d = 83.3m. The answer to b would be mostly the same work switching up the sin/cos. Does that work?
Your idea is correct. Your equation for Uk is dimensionally inconsistent. If you find the correct coefficient of friction, then you can find the stopping distance up and down the plane.
 
  • #3
Oops, I meant Uk = V^2 /(2gs) not ag. Sorry. This, I think, fixes the inconsistency problem. Was the rest of my work ok?
 
  • #4
inner08 said:
Oops, I meant Uk = V^2 /(2gs) not ag. Sorry. This, I think, fixes the inconsistency problem. Was the rest of my work ok?
Looks good for down the plane. Up the plane is not switching sin and cos. It is just getting the forces actin in the right direction.
 

1. How long does it take to stop a car traveling at 100km/h on a flat surface?

The stopping distance of a car depends on several factors, including the mass of the car, the efficiency of its brakes, and the condition of the road. On a flat surface, it typically takes a car traveling at 100km/h between 45-55 meters to come to a complete stop. This is assuming the car has good brakes and the road is dry and in good condition.

2. Can different types of cars have different stopping distances at the same speed?

Yes, the stopping distance of a car can vary depending on its mass, braking system, and tire grip. For example, a heavier car will require a longer distance to stop compared to a lighter car. Similarly, a car with better brakes and tires will be able to stop in a shorter distance compared to a car with worn out brakes and tires.

3. How does the slope of the road affect the stopping distance?

The slope of the road can significantly affect the stopping distance of a car. If the road is inclined, it will take longer for the car to stop as it will have to overcome the force of gravity. On the other hand, if the road is declined, the car will be able to stop in a shorter distance due to the force of gravity aiding the braking process.

4. How does the speed of the car affect the stopping distance?

The speed of the car has a direct impact on the stopping distance. The higher the speed, the longer the stopping distance will be. This is because the car will have more kinetic energy that needs to be dissipated, which requires more time and distance. For example, a car traveling at 200km/h will require four times the stopping distance of a car traveling at 100km/h.

5. Can weather conditions affect the stopping distance?

Yes, weather conditions can significantly impact the stopping distance of a car. On a wet or icy road, the tires have less grip, making it harder for the car to stop. This means it will require a longer distance to come to a complete stop compared to a dry road. Additionally, rain, snow, or fog can also decrease visibility, making it harder for the driver to react and brake in time.

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