Acceleration Derivations Many of you remember the old 'DiRT' formula. Distance = Rate times Time.

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Presentation transcript:

Acceleration Derivations Many of you remember the old 'DiRT' formula. Distance = Rate times Time

Scientifically, it's 'average velocity' equals distance divided by time. v (av) = d/t or v (av) = (v i + v f ) / 2

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

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?

Acceleration is the change of speed or direction per unit time. So, we can begin with the definition of average velocity. v (av) = (v i + v f ) / 2 By Definition for acceleration: a = {v f - v i } / t Rearranging and solving v f = v i + at

Take d = v (av) t Take the expanded version of v (av) and insert it into the v(av) above. d= {(v i + v f ) / 2)} t

Insert (v i + at) for v f in d = {(v i + v f ) / 2)} t find d = { (v i + v i + at )/ 2 } t

Collect terms and get d= v i t + 1/2 at 2

New derivation: d = v av t and substitute for v av d = {(v i + v f ) /2 } t Now, substitute for t with = {v f - v} / a

So, d = {(v i + v f ) /2 } {v f - v i } / a Simplify:

d = { vf 2 - vi 2 - vivf + vivf } / 2a

2ad = vf 2 - vi 2 vf 2 = vi 2 + 2ad

Find: the acceleration of the TekBot