www.VirtualNerd.com

How do you find the change in time given constant work and increased power?

A cyclist delivers 1000 Watts of power to her bike wheels when she speeds up from 5 meters per second all the way to 15 meters per second in just 12 seconds. How many seconds would it take to speed up the same amount, if she were able to deliver twice the power to the wheels?

Summary

  1. viA- initial speed for case A
  2. vfA- final speed for case A
  3. P-power
  4. t- time
  5. m- meters
  6. s- seconds
  7. B- Case B is the set up where the cyclist uses twice the power to speed up her bike
  8. viB- initial speed for case B
  9. vfB- final speed for case B

Notes

    1. P- power
    1. W- work
    2. ∆KE- change in kinetic energy
    1. ∆KE- change in kinetic energy
    2. m- mass
    3. vf- final speed
    4. vi- initial speed
    1. ∆KEA- Change in kinetic energy for case A
    2. ∆KEB- Change in kinetic energy for case B
    3. WA- work done on bike in case A
    4. WB- work done on bike in case B
    5. The work-energy theorem gaurantees that the cyclist performs the same amount of work on the bike in both cases!
    1. P- power
    1. P- power
    2. W- work
    1. Inverse factors means that if power is multiplied by 2, then time is divided by 2. This works as long as work is constant!
    1. P- power
    2. t- time
    1. t- time
    2. s- seconds
    1. With double the power, the same work is done in half the time!