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

[fatla00]

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!

 

[Dick]

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=?