Find minimum stopping distance of a car

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SUMMARY

The minimum stopping distance of a car moving at 32.0 m/s is calculated using the principles of physics, specifically the equations of motion and the concept of kinetic energy. Given that a car requires 66.64 m to stop from an initial speed of 14.0 m/s, the stopping distance increases with the square of the speed. By applying the formula for stopping distance, which is proportional to the square of the initial velocity, the minimum stopping distance for 32.0 m/s can be determined to be approximately 266.56 m.

PREREQUISITES
  • Understanding of basic physics concepts, particularly kinematics
  • Familiarity with the equations of motion
  • Knowledge of frictional forces and their impact on stopping distances
  • Ability to manipulate algebraic equations for solving problems
NEXT STEPS
  • Study the equations of motion, particularly the formula for calculating stopping distance
  • Learn about the role of friction in vehicle dynamics
  • Explore kinetic energy concepts and their relation to stopping distances
  • Investigate real-world applications of stopping distance calculations in automotive safety
USEFUL FOR

Students studying physics, automotive engineers, and anyone interested in vehicle safety and dynamics will benefit from this discussion.

evan b
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1. Homework Statement

It takes a minimum distance of 66.64 m to stop a car moving at 14.0 m/s by applying the brakes (without locking the wheels). Assume that the same frictional forces apply and find the minimum stopping distance, when the car is moving at 32.0 m/s.




The Attempt at a Solution



i'm confused on what to do here... i thought it might be as simple as setting them equal to each other and solving for the distance. we know the mass of the car is the same so that isn't a factor. for the first we know Vi=14 m/s and Vf = 0, and the second time its velocity is Vi=32 m/s and Vf = 0. I'm not sure where to go from here...
 
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