How long does it take to stop the car

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SUMMARY

The discussion focuses on calculating the stopping distance of a car moving at 14 m/s with a coefficient of friction of 0.8. The process involves drawing a free-body diagram (FBD) to identify the forces acting on the car, specifically the weight, friction, and normal force. The equation 4f = ma is used to derive acceleration, followed by the kinematic equation Vf² = Vi² + 2*a*d to solve for the stopping distance (d) with final velocity (Vf) set to 0. A tutorial link is provided for further learning.

PREREQUISITES
  • Understanding of free-body diagrams (FBD)
  • Knowledge of Newton's second law (4f = ma)
  • Familiarity with kinematic equations (Vf² = Vi² + 2*a*d)
  • Basic concepts of friction and its coefficient
NEXT STEPS
  • Study the principles of free-body diagrams in physics
  • Learn more about Newton's laws of motion
  • Explore kinematic equations in-depth, focusing on their applications
  • Investigate the effects of different coefficients of friction on stopping distances
USEFUL FOR

This discussion is beneficial for physics students, automotive engineers, and anyone interested in understanding vehicle dynamics and stopping distances.

bob4000
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if a car is moving at 14m/s, and the coefficient of friction is 0.8, what is the distance it takes to stop the car after the brakes are applied locking all four wheels?
 
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The first step in the problem is to draw your free-body diagram and label all of the forces acting on the car.
Basically you have 3 forces, the force of the weight, the force of friction, and the normal force on each tire.
Because each of these forces are the same on each wheel it is only neccesary to draw the FBD for one wheel.
After you draw your FBD set up your force equation in each direction. In this case the car is is only moving in 1 direction call it the positive X direction.
So you have your sum of the forces in the X direction equation.
4f=ma
where is the friction force

solve that equation for a and then use the kinematic equation Vf^2=Vi^2+2*a*d

with Vf=0 solve for d
 

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