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Answer:
a) at t=12, Whitney is speeding up
b) 13/48 = 0.2704833 . . . miles/min; not a good measure
Step-by-step explanation:
a) At t=12, Whitney's velocity is -0.2 miles/min and is decreasing. That is, the magnitude of her velocity (speed) is increasing. Whitney is speeding up at t=12.
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b) The (signed) area under the curve, divided by the time period (24 min) will give Whitney's average velocity. It can be found by using the formulas for area of a trapezoid and triangle.
distance 0-11 = 1/2(11 +3)(0.8) = 5.6 miles
distance 11-16 = 1/2(5)(-0.6) = -1.5 miles
distance 16-24 = 1/2(8)(0.6 = 2.4 miles
Whitney's average velocity is ...
(5.6 -1.5 +2.4)mi/(24 min) = 6.5 mi/(24 min) = (13/48) mi/min ≈ 0.270 mi/min
The laws of physics tell us that no work is being done if velocity is constant. Hence, the strenuousness of Whitney's pedaling depends on the acceleration she is maintaining. The average velocity measure tells nothing of that, so is a poor measure of how strenuously Whitney is pedaling.
