Part B: Deducing kinematic parameters from the object trajectory

In Part A$,$ you were given trajectories of four dropping ball experiments. You have computed the average trajectory. Starting from these results, please complete the following exercise $($Hint: Try using a FOR loop$)$:

$($B$1)$ Create a "test" particle trajectory. Ask MATLAB to create a $2$D matrix where the first column is time and the second column is position. Please make the time column linear and the position column sinusoidal. The matrix should be long enough to contain at least $3$ periods.

$($B$2)$ Develop an algorithm to compute the first derivative. $($i$)$ Calculate velocity of the test trajectory $($ii$)$ Calculate velocity of the ball drop data.

$($B$3)$ Develop an algorithm to compute the second derivative. $($i$)$ Calculate acceleration of the test trajectory $($ii$)$ Calculate acceleration of the ball drop data.

$($B$4)$ Create two graphs. The first graph should contain plots the position, velocity, and acceleration of the test trajectory. The second graph should contain plots of the position, velocity and acceleration of the ball drop data.