Question

[need math help] Study buddies part #3

Answer 1

9514 1404 393

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.