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course Mth 271
The velocity of an automobile coasting down a hill is given as a function of clock time by v(t) = .001 t^2 + .14 t + 1.8, with v in meters/sec when t is in seconds. Determine the velocity of the vehicle for clock times t = 0, 15 and 30 sec and make a table of rate vs. clock time.Sketch and label the trapezoidal approximation graph corresponding to this table and interpret each of the slopes and areas in terms of the situation.
*** I don’t know how to draw a graph on the computer.
@& You can list the quantities you labeled when you constructed the graph. I don't need to see graphs, I do need to see your descriptions or (in this case) the quantities you get from the graphs.*@
Evaluate the derivative of the velocity function for t = 22.5 sec and compare with the approximation given by the graph.
By how much does the antiderivative function change between t = 0 and t = 30 seconds, what is the meaning of this change, and what is the graph's approximation to this change?
V(0) = 1.8
V(15) = 4.125
V(30) = 6.9
Y’ = 0.002t + 0.14
Y’(0) = 0.14
Y’(15) = 0.17
Y’(30) = 0.2
t(22.5) = 0.1844
The antiderivative function changes by 6.9 - 1.8 = 5.1
It means that the velocity of the car is increasing with time.
@& You need to begin this by constructing the trapezoidal approximation graph and giving the results you obtain from that graph.*@
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