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How do you find the change in breaking distance of an object that brakes to a stop if the initial speed changes?

You're driving along in your car with a speed of 15 meters per second. When you slam on your brakes, you find that it takes 40 meters of skidding until you stop. How far would you skid if instead of starting with a speed of 15 meters per second, you started with a speed of 30 meters per second?

Summary

  1. A- Case A is where the car skids 40 meters
  2. viA- initial speed in case A
  3. vfA- final speed in case A
  4. dA- skidding distance in case A
  5. m- meters
  6. s- seconds
  7. B- Case B is where the car starts out going faster
  8. viB- initial speed in case B
  9. vfB- final speed in case B
  10. dB- skidding distance in case B
  11. Ffr- force of friction

Notes

    1. W- work
    2. ∆KE- change in kinetic energy
    1. Ffr- force of friction
    2. d- distance
    3. KEi- initial kinetic energy
    1. Ffr- force of friction
    2. d- distance
    3. m- mass
    4. vi- initial speed
    1. d- distance
    1. viB- initial speed in case B
    2. viA- initial speed in case A
    3. m/s- meters per second
    1. viA- initial speed in case A
    2. dA- distance in case A
    1. dB- distance in case B
    1. dB- distance in case B
    2. dA- distance in case A
    3. m- meters
    1. If the car speed tripled, the skidding distance would increase by 32, or 9