Acceleration Derivations

1
Acceleration Derivations

• Many of you remember the old 'DiRT' formula.
  
• Distance Rate times Time

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• Scientifically, it's 'average velocity' equals
  distance divided by time.
• v (av) d/t or
• v(av) (vi vf) / 2

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• Taking measurements from a sample Quicktime movie
  of the TekBot,
• velocity v(av) d / t
• 8.5 cm / 0.3 sec 28.33 cm/sec

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• What will you use to find the velocity of the
  TekBot?
• How does the velocity that you found compare
  with the velocity from the movie?

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• Acceleration is the change of speed or direction
  per unit time. So, we can begin with the
  definition of average velocity.
• v(av) (vi vf) / 2
• By Definition for acceleration
• a vf - vi / t
• Rearranging and solving
• vf vi at

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• Take d v(av) t

Take the expanded version of v(av) and insert it
into the v(av) above. d (vi vf) / 2) t

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• Insert (vi at) for vf in d (vi vf) / 2)
  t
• find d (vi vi at )/ 2 t

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• Collect terms and get
• d vi t 1/2 at2

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• New derivation
• d vav t and substitute for vav
• d (vi vf) /2 t
• Now, substitute for t with
• vf - v / a

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• So, d (vi vf) /2 vf - vi / a

Simplify
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• d vf2 - vi2 - vivf vivf / 2a

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• 2ad vf2 - vi2
• vf2 vi2 2ad

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• Find the acceleration of the TekBot