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Calculus/Acceleration or Velocity

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Expert: - 12/10/2008


Question
Mary has been practicing to race in a 10 kilometer race.  She would run every day.  At the beginning of her practice, her time for the race dropped rapidly, but after an initial rapid drop in time, her time for the race has been declining at a much slower rate. Let R(d) be the curve which best represents Mary's winning race times on day d of her practice. Which of the following is negative?  

I. R(d) II. R'(d)  III. R''(d)  

Answer
R(d) can't be negative since R(d) is the distance she travelled.

R"(d) is the rate of change in velocity, and velocity has been decreasing at a slower rate, which means the R"(d) is increasing.

R'(t) is the speed, and that has been decreasing, so it's the only one that could be negative.

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