Solve the Exponential Question: Breaking Distance at 60 km/h

In summary, the conversation discusses the relationship between a car's traveling speed and its stopping distance in an emergency stop. It is determined that if the traveling speed doubles, the stopping distance will be four times the original distance. The conversation also provides a scenario where a car traveling at 40 km/h can stop in 3 meters, and the question is posed on what the stopping distance would be if the speed was increased to 60 km/h. The solution is not provided, but the concept of kinetic energy and braking force is mentioned as a way to solve the problem. The conversation concludes with a statement about the relationship between velocity and kinetic energy.
  • #1
fatla00
1
0
Exponential Question??

Homework Statement



If a car traveling at a speed of V can break at an emergency stop at a distance X. Assuming all other conditions are similar if the traveling speed of the car doubles, the stopping speed will be 4x. (I worked that out)
A driver traveling at 40 km/h in a school zone can break to emergency stop in 3 meters. What would be the breaking distance of the car were traveling at 60 km/h.

2. The attempt at a solution

I have no idea how to figure this out. From what I've done, I think the number is going to be less the 7.5 but greater than 6. I'm not exactly sure how I got that though.

Any help would be Greatly Appreciated!
 
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  • #2
If you solved the first one by equating the kinetic energy to a constant braking force times distance then you understand the problem. Doubling the velocity multiplies the kinetic energy by four. I don't understand why multiplying the velocity by 1.5 is throwing you for a loop. 2^2=4, 1.5^2=?
 

What is an exponential question?

An exponential question is a type of mathematical question that involves solving for a variable in an exponential equation. In these equations, the variable appears in the exponent, making the solution more complex than a linear equation.

What is breaking distance?

Breaking distance is the distance a vehicle travels from the moment the brakes are applied to the moment the vehicle comes to a complete stop. It is influenced by factors such as the vehicle's speed, reaction time of the driver, and road conditions.

How is breaking distance calculated at 60 km/h?

Breaking distance at 60 km/h can be calculated using the formula d = (v^2)/(2a), where d is the breaking distance, v is the initial velocity (60 km/h), and a is the deceleration rate. The deceleration rate can vary depending on the vehicle and road conditions.

Why is it important to solve for breaking distance at 60 km/h?

Breaking distance is an important factor to consider in driving and road safety. By solving for breaking distance at 60 km/h, we can understand the distance a vehicle needs to stop at this speed, which can help inform safe driving practices and road design.

How can exponential questions be applied to other real-life situations?

Exponential questions can be applied to various situations such as population growth, compound interest, and radioactive decay. These equations allow us to make predictions and understand the behavior of quantities that change exponentially over time.

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