Braking Distance Increase Factor w/ 50% Speed Increase

  • Thread starter sugarntwiligh
  • Start date
In summary, the conversation discusses the impact of increasing the speed of a car by 50% on its minimum braking distance. The equation provided (0.5(2m)(v1+5.0)^2 = 0.5m(v2+5.0)^2) helps deduce the answer of 2.25, by simplifying and eliminating time as a variable. It is also explained that if the speed is 50% greater, the kinetic energy will be 2.25 times greater than before.
  • #1
sugarntwiligh
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Homework Statement



If the speed of a car is increased by 50%, by what factor will its minimum braking distance be increased, assuming all else is the same? Ignore the driver's reaction time.

Homework Equations




.5(2m)(v1+5.0)^2 = .5m(v2+5.0)^2

I know the answer is 2.25 and is deduced from the above equation. I tried to simplify:

v1^2+10v1+25 = .5v2^2+5v2+12.5

but I am still confused. I know I should eliminate time as a variable, but I am unsure of how to do this.
 
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  • #2
sugarntwiligh said:
.5(2m)(v1+5.0)^2 = .5m(v2+5.0)^2
I don't understand what this equation represents.

Try this:

KE_1 = 1/2 m (v_1)^2

KE_2 = 1/2 m (v_2)^2

If v_2 is 50% greater than v_1 (express that mathematically), how does KE_2 compare with KE_1?
 
  • #3
So,
(v_1) = (v_2) + (v_2 * 0.5) = 1.5 (v_2)
and, if I substitute KE_1 and KE_2 into the equation,
I get KE_1=2.25KE_2.
OMG THANK YOU!
 

1. What is the braking distance increase factor with a 50% speed increase?

The braking distance increase factor with a 50% speed increase refers to the amount that the braking distance will increase when the speed is increased by 50%. This factor is commonly used in scientific and engineering calculations to determine the necessary braking distance for a vehicle or object.

2. How is the braking distance increase factor calculated?

The braking distance increase factor is calculated by taking the square root of the speed increase percentage. For example, if the speed is increased by 50%, the braking distance increase factor would be the square root of 50%, which is approximately 1.41.

3. Why is the braking distance increase factor important?

The braking distance increase factor is important because it helps determine the necessary braking distance for a vehicle or object. This information is crucial for safety purposes and can help prevent accidents by ensuring that the vehicle or object has enough space to come to a complete stop.

4. How does the braking distance increase factor affect braking systems?

The braking distance increase factor directly affects braking systems by determining the amount of time and distance needed for a vehicle or object to come to a complete stop. A higher factor means that the braking system needs to be more powerful and efficient to bring the vehicle or object to a stop in a shorter distance.

5. Are there other factors that can affect the braking distance besides speed?

Yes, besides speed, there are other factors that can affect the braking distance, such as the condition of the road, weather conditions, the weight and load of the vehicle, and the type and condition of the braking system. These factors should also be taken into account when calculating the necessary braking distance.

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