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# 3.4Done - 3.4 Velocity and Other Rates of Change...

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3.4 Velocity and Other Rates of Change Instantaneous Rate of Change f ¢ H a L = lim h Æ 0 f H a + h L - f H a L ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ h Velocity, Speed, and Acceleration If the position function is described by s H t L , then velocity = v H t L = s ¢ H t L speed = » v H t L » = » s ¢ H t L » acceleration = a H t L = v ¢ H t L = s ¢¢ H t L Free - fall Constants on Earth English units Æ s = - 16t 2 a = - 32 ft ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ sec 2 Metric units Æ s = - 4.9t 2 a = - 9.8 m ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ sec 2 Marginal Cost Marginal Cost is the derivative of the Cost function. 1. A particle moves along a line so that its position at any time t 0 is given by s H t L = t 2 - t - 4, where s is measured in meters and t is measured in seconds. Find H a L the displacement in the first 3 seconds H b L the average velocity in the first 3 seconds H c L the acceleration at t = 3 seconds H d L where the particle is when s is a minimum H e L the velocity when t = 3 seconds H a L s H 3 L - s H 0 L = 2 - H - 4 L = 6 meters H b L average velocity = 6 meters ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ

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