Write a function called penMotion. It should take two arrays as input, one containing the x$-$

coordinates of the pen stroke, and one containing the $y-$coordinates. The function should

return two arrays. The first should contain the arc$-$length value of each point on the stroke,

and the second should contain the pen speed at each point. The values must be returned in

that order.

The arc length, $s(i),$ of the $i^{th}$ point on the stroke is computed as:

$s_i=s_{i-1}+\sqrt[\phantom{2}]{(x_i-x_{i-1}{)}^2+(y_i-y_{i-1}{)}^2}$

The first data point has an arc length value of zero.

The speed, $v(i),$ of the $i^{th}$ point on the stroke is computed as:

$v_i=\frac{\sqrt[\phantom{2}]{(x_i-x_{i-1}{)}^2+(y_i-y_{i-1}{)}^2}}{t_i-t_{i-1}}$

where $t_i-t_{i-1}$ is the time between the two data points, which we will assume is $1.($This

assumption is valid if the data points are sampled at a constant rate.$)$ Also, assume that the

first point on the stroke has a speed of zero, as it is not possible to calculate the speed using

this equation.

Hint: Your loops for computing arc length and speed should exclude the first data point on

the stroke.