An object is thrown directly downward from the top of a cliff. The distance that the object has fallen in meters after t seconds is given by the function d(t) = 5t + 4.9t2, t ≥ 0. a) Determine the average rate of change of the distance fallen for each interval. i) 0 ≤ t ≤ 3ii) 2 ≤ t ≤ 4iii) 3 ≤ t ≤ 5 b) Sketch a graph of the function on a separate sheet of paper.  c) Use a difference quotient to estimate the instantaneous rate of change of the distance fallen at each time. i) t = 2 sii) t = 4 s

Physics for Scientists and Engineers: Foundations and Connections
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Author:Katz, Debora M.
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Chapter2: One Dimensional Motion
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An object is thrown directly downward from the top of a cliff. The distance that the object has fallen in meters after t seconds is given by the function d(t) = 5t + 4.9t2, t ≥ 0.

a) Determine the average rate of change of the distance fallen for each interval. 
i) 0 ≤ t ≤ 3
ii) 2 ≤ t ≤ 4
iii) 3 ≤ t ≤ 5

b) Sketch a graph of the function on a separate sheet of paper. 

c) Use a difference quotient to estimate the instantaneous rate of change of the distance fallen at each time. 
i) t = 2 s
ii) t = 4 s

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