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# Calc03_4 - 3.4 Velocity Speed and Rates of Change Photo by...

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3.4 Velocity, Speed, and Rates of Change Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2008 Denver & Rio Grande Railroad Gunnison River, Colorado

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Consider a graph of displacement (distance traveled) vs. time. time (hours) distance (miles) Average velocity can be found by taking: change in position change in time s t = t s A B ( 29 ( 29 ave f t t f t s V t t + ∆ - = = The speedometer in your car does not measure average velocity, but instantaneous velocity. ( 29 ( 29 ( 29 0 lim t f t t f t ds V t dt t ∆ → + ∆ - = = (The velocity at one moment in time.)
Velocity is the first derivative of position.

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Example: Free Fall Equation 2 1 2 s g t = Gravitational Constants: 2 ft 32 sec g = 2 m 9.8 sec g = 2 cm 980 sec g = 2 1 32 2 s t = 2 16 s t = 32 ds V t dt = = Speed is the absolute value of velocity.
Acceleration is the derivative of velocity. dv a dt = 2 2 d s dt = example: 32 v t = 32 a = If distance is in: feet Velocity would be in: feet sec Acceleration would be in: ft sec sec 2 ft sec =

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time distance
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