**Transcription for Educational Website**---### Particle Motion ProblemConsider the table of values for a particle, \( A \), moving along the x-axis. The movement is modeled by a twice-differentiable function \( p \), where time \( t \) is in seconds and position \( p(t) \) is in feet. The selected values are provided below:| \( t \) (seconds) | 0 | 3 | 6 | 9 | 12 ||-------------------|---|---|---|---|----|| \( p(t) \) (feet) | 3 | 5.5 | 7 | 13 | 17 |**(a)** Use a midpoint Riemann sum with two subintervals of equal length and the given table values to approximate the value of \(\int_{0}^{12} p(t) \, dt\). Show your computations.**(b)** Using the data in the table, approximate \( p'(10) \) by calculating the average rate of change of \( p(t) \) over the interval \( 9 \leq t \leq 12 \). Show your calculations, including the units.**(c)** Interpret the meaning of \( p'(10) \) within the context of this problem.---

Name: **Transcription for Educational Website**---### Particle Motion Probl
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: **Transcription for Educational Website**---### Particle Motion ProblemConsider the table of values for a particle, \( A \), moving along the x-axis. The movement is modeled by a twice-differentiable function \( p \), where time \( t \) is in second