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Copy_of_3.4notestouse1 - 3.4 Velocity and Other Rates of...

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Calculus Section 3.4 Page19 3.4 Velocity and Other Rates of Change Remember slope of secant line slope of tangent line (diagram) Average velocity = distance traveled total time (assume you are going in one direction) What is this like? Suppose you drive your car for 2 h and travel exactly 80 mi. What is your average velocity ? Instantaneous velocity = first derivative of the distance function = s'(t) = ds dt What is this like? In the Calculus AP course, we are just concerned with rectilinear motion (motion of a particle along a line) Summary s(t) gives position s'(t) =0 ___________ s'(t) gives velocity s'(t) > 0___________ s'(t) < 0___________
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Calculus Section 3.4 Page 20 Example 1 s(t) = t 3 – 6t 2 + 9t (t is measured in sec, s is measured in ft) a) find the velocity at time t b) what is the velocity after 2 sec, after 4 sec? c) when is the particle at rest? d) when is the particle moving to the right (in a positive direction)? e) draw a diagram to represent the position of the particle for t 0 on a number line.
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