Generic KE problem with a twist.

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SUMMARY

The discussion centers on a physics problem involving kinetic energy (KE) and braking distances of two cars traveling at different speeds. The key takeaway is that the car traveling at half the velocity requires one-fourth the distance to stop compared to the faster car, despite the lack of information on mass and braking capability. The kinetic energy formula, KE = 1/2m·v^2, is crucial in understanding the relationship between speed and stopping distance. The conclusion drawn is that the braking distance is influenced by the square of the velocity, which explains the discrepancy in the answers provided.

PREREQUISITES
  • Understanding of Kinetic Energy (KE) and its formula KE = 1/2m·v^2
  • Basic knowledge of physics concepts related to motion and braking
  • Familiarity with the relationship between speed, mass, and stopping distance
  • Concept of friction force and its role in braking
NEXT STEPS
  • Study the relationship between velocity and stopping distance in physics
  • Learn about the factors affecting braking distances, including mass and friction
  • Explore real-world braking performance comparisons of different vehicles
  • Investigate the implications of kinetic energy in collision scenarios
USEFUL FOR

This discussion is beneficial for physics students, educators, automotive engineers, and anyone interested in understanding the dynamics of vehicle motion and braking efficiency.

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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).
 
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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?
 
Last edited:

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