I want to find a parameterization for a point moving on an Achemedean spiral with a constant tangential velocity. If I let t be my parameter, it is easy to find a parameterization for a point on a Achemedean spiral but it tangental velocity increases as t increases. This is what I have so far.
x(t)=tcos(t)
y(t)=tsin(t)
v_t=sqrt(v_x^2+v_y^2)
where v_t is the tangential velocity. Is there some parameterization x(t) and y(t) that when I take the derivative and find its magnitude(tangential velocity), it remains constant?