Generic KE problem with a twist.

[Fungiefips]

Homework Statement

"Two cars are traveling along a road, and one is going at half the velocity of the other one. What is the distance required to come to a stop for the car going at the slower speed relative to the faster car."

The possible answers listed were as:
A:1/2 the distance
B:1/4 the distance
C:Not enough info provided

Homework Equations

I suppose it would be KE=1/2m·v^2

The Attempt at a Solution

At first glance I plugged in a mass of 2000kg for each and a speed of 20m/s for the fast one and 10m/s for the slow one. The resulting KE's came out to be 40,000 and 10,000 respectively. However after reading the problem I discovered that it was not stated that the masses were equal, so I answered not enough info. Upon receiving my test back, lo and behold my teacher marked that B was in fact correct. My question is, how is it possible to calculate the braking distance without knowing the masses of the cars, and without also knowing the braking capability of each car. i.e. A Ferrari Enzo can brake from 60-0 in 109 ft, whereas a 2005 Volkswagen Jetta takes 130 ft. to stop 60-0 (both cars weighing 3230 lbs).

 

[berkeman]

Great question. Your initial intuitive answer is the same as mine, but maybe increasing mass increases the F=mu*N friction force enough to offest it in the ideal?

 

[m2003]

I would argue that without knowing the masses and braking capabilities of the cars, it is not possible to accurately calculate the distance required for the slower car to come to a stop relative to the faster car. This is because the kinetic energy equation, KE=1/2mv^2, depends on both the mass and velocity of an object. Without knowing the mass of the slower car, it is not possible to accurately calculate its kinetic energy, and therefore the distance required for it to come to a stop.

Additionally, the braking capabilities of the cars also play a crucial role in determining the stopping distance. As mentioned in the example of the Ferrari Enzo and Volkswagen Jetta, even cars with similar masses can have vastly different braking distances. Therefore, without knowing the braking capabilities of the cars, it is not possible to accurately determine the distance required for the slower car to come to a stop relative to the faster car.

To accurately solve this problem, more information is needed such as the masses and braking capabilities of the cars. Without this information, it is not possible to provide a definite answer and the correct response would be "not enough information provided".