The velocity of an automobile coasting down a hill is given as a function of clo

Question

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.

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?

The best answer for this question should show all work and include a sketch of the trapezoidal approximation graph.

Explanation / Answer

Velocity at clock times:

v(0) = .001(0)^2 + .14(0) + 1.8 = 1.8 m/s

v(15) = .001(15)^2 + .14(15) + 1.8 = 4.125 m/s

v(30) = .001(30)^2 + .14(30) + 1.8 = 6.9 m/s

Derivative of velocity function:

v(t) = .001t^2 + .14t + 1.8

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