# L14 - L14 Rates of Change in the Natural and Social...

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L14 – Rates of Change in the Natural and Social Sciences Recall Average Rate of Change Instantaneous Rate of Change If s = f ( t ) is the position of a particle moving in a straight line, then 1

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Suppose the position of a particle is given by s = f ( t ) = t 3 - 9 t 2 + 24 t where t is measured in seconds and s in meters. a) Find the velocity of the particle at any time t . b) Find the velocity at t = 1 and t = 3 seconds. 2
c) When is the particle at rest? d) When is the particle moving in a positive direction? 3

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e) Draw a diagram to represent the motion of the particle. f) Find the total distance moved in the ﬁrst ﬁve seconds. 4
A dynamite blast blows a heavy rock straight up with a velocity of 160 ft/sec. Its height at any time t is f ( t ) = 160 t - 16 t 2 . a) Find its velocity at any time t . b) What is the maximum height reached by the rock? 5

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up and on the way down). 6
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## This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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L14 - L14 Rates of Change in the Natural and Social...

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