If coordinate vector of a point is given by

coor[t_] := {Quantity[x[t], "Meters"], Quantity[y[t], "Meters"]}

and time is defined as

time = Quantity[t, "Seconds"]

and constant speed as

speed = Quantity[c, "Meters"/"Seconds"]

then time derivative of coordinate vector will give velocity in proper units:

D[coor[t], time]

which also can be rescaled as dimensionless

D[coor[t], time]/speed

Degrees are dimensionless. So they do not interfere with dimensioned units.

Thank you so much, Sam. Your example will motivate me to start using units, which I have avoided to date!

I had to back out of units. While convenient - I could always print speed as miles per hour without referring to the underlying data - the cost in execution time was significant. (Example coming - someday)