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course Mth 173
6/23/13~around 10PM
Week 4 Quiz 2 Version 3The velocity of an automobile coasting down a hill is given as a function of clock time by v(t) = .00092 t^2 + .69 t + 1.5, with v in meters/sec when t is in seconds. Determine the velocity of the vehicle for clock times t = 0, 8 and 16 sec and make a table of rate vs. clock time.
0 1.5
8 7.08
16 12.8
Sketch and label the trapezoidal approximation graph corresponding to this table and interpret each of the slopes and areas in terms of the situation.
-->a = vAve * Dt = 7.15m/s * 16s = 114.4m
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vAve = `ds / `dt so
`ds = vAve * Dt = 7.15m/s * 16s = 114.4m
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first slope = (7.08 - 1.5) / (8 - 0) = .698 m/s/s
second slope = (12.8 - 7.08) / (16 - 8) = .715 m/s/s
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Good. These are average accelerations.
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Evaluate the derivative of the velocity function for t = 12 sec and compare with the approximation given by the graph.
-->r(t) = .00184(12) + .69 = .71
By how much does the antiderivative function change between t = 0 and t = 16 seconds, what is the meaning of this change, and what is the graph's approximation to this change?
12.8 m/s - 1.5 m/s = 11.3 m/s ; this shows that the velocity has increased 11.3 meters per second over the time interval of 16 seconds
&#This looks good. See my notes. Let me know if you have any questions. &#