8. (seconds) 0. 3 6 9 12 p(t) (feet) 3 5.5 7 13 17 The position of a particle, A, moving along the x-axis is modeled by a twice-differentiable function P, where time t is measured in seconds and p (t) is measured in feet. Selected values of p (t) are shown in the table above. (a) Use a midpoint Riemann sum with two subintervals of equal length and values from the table to 12 approximate the value of p (t)dt Show the computations that lead to your answer. (b) Use the data in the table to approximate p' (10) using the average rate of change of p (t) over the interval 9 < t < 12. Show the computations that lead to your answer. Indicate units of measure.

Question

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8.
(seconds)
0. 3
6 9 12
p(t)
(feet)
3 5.5 7 13 17
The position of a particle, A, moving along the x-axis is modeled by a twice-differentiable function P,
where time t is measured in seconds and p (t) is measured in feet. Selected values of p (t) are shown in
the table above.
(a) Use a midpoint Riemann sum with two subintervals of equal length and values from the table to
12
approximate the value of
p (t)dt Show the computations that lead to your answer.
(b) Use the data in the table to approximate p' (10) using the average rate of change of p (t) over the
interval 9 < t < 12. Show the computations that lead to your answer. Indicate units of measure.
Expand
Transcribed Image Text

8. (seconds) 0. 3 6 9 12 p(t) (feet) 3 5.5 7 13 17 The position of a particle, A, moving along the x-axis is modeled by a twice-differentiable function P, where time t is measured in seconds and p (t) is measured in feet. Selected values of p (t) are shown in the table above. (a) Use a midpoint Riemann sum with two subintervals of equal length and values from the table to 12 approximate the value of p (t)dt Show the computations that lead to your answer. (b) Use the data in the table to approximate p' (10) using the average rate of change of p (t) over the interval 9 < t < 12. Show the computations that lead to your answer. Indicate units of measure.

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