A UFO has been spotted in the Salt Lake airspace and is being tracked by radar in polar coordinates $r$

and $.$ The data recorded is given in the following table

Table $1$: Radial and angular location of UFO as a function of time

Naturally, the radar automatically calculates the speed and acceleration of the UFO but that part of

the radar system has been dysfunctional for a while. You are one of the engineers running the radar

station and the governor has tasked you to find the speed and acceleration of the UFO.

Use second order finite differencing to find the vector expressions for the velocity $u$ and acceler$-$

ation a of the UFO at $t=210s.$ Recall that the velocity and acceleration in polar coordinates are

given by:

$u=r^{}{e}_r+r{}^{}{e}_{}$;$,a=((r^{})-r{}^{}{?}^2)e_r+(r{}^{}+2r^{}{}^{})e_{},$

where $r^{}=\frac{dr}{(d)t},{}^{}=\frac{d}{dt},$ etc... and $e_r$ and $e_{}$ are unit vectors in the radial and tangential directions,

respectively. Do this $"$by hand" and typeset it into Python $($markdown $+$ LaTeX$).$ Note that you

can find second order finite difference formulas for first and second derivatives on the slides $-$ use

the formula that is most suitable to solve this problem.