For this problem, you are to submit a single Excel workbook with your calculations on one sheet and graphs of velocity vs$.$ time, and position vs$.$ time on separate sheets. The calculations will be similar to the robot problem from Class $23($last Thursday$),$ except that the accelerations are given as equations rather than measured data points.

On your calculation sheet, format the velocity cells to show one decimal place and the position cells to show no decimal places $($integers$).$ Your graphs should have titles and labeled axes, with units. The velocity and position should be plotted as smooth curves without data markers. $($Since the accelerations are equations, you should not show data markers. The problem that we worked in class had measured acceleration data, so data markers were shown for those graphs.$)$

Use time increments of $1$ second or less. For comparison purposes, here are the exact values of the maximum speed and distance between the stations:

Maximum speed $=31\mathrm{.}8\frac{m}{s},$ Distance $=637m$

$($Problem $9\mathrm{.}9$ from text$)$ Abrupt changes in acceleration cause high values of jerk, which is the rate of change of acceleration. To produce a smooth ride, a subway train accelerates and decelerates between two stations with these acceleration profiles:

For the first $10$ seconds: $a=5\mathrm{.}0sin(\frac{t}{10})\frac{m}{s^2}$

For the next $10$ seconds, the train runs at a constant speed