Undergrad Arc Length Parameterization for Unit Circle: Cos(s) & Sin(s)

[rabbed]

(cos(s), sin(s)) gives an arc-length parameterization of the unit circle so that the speed is constantly 1, but the second derivative doesn't give zero acceleration which should be the case with constant speed?

 

[jedishrfu]

THe speed is constant but you are constantly turning too right?

Acceleration is defined as the rate of change of velocity per unit time and since the velocity vector is changing direction then there's an acceleration that is not zero.

 

[rabbed]

Ah, right.. tricky
Thanks

 

[rabbed]

Does this mean that a vector which is a function of t and that vector has unit length for all t, will always be perpendicular to its integrated vector or can you only say that it's derivative will be perpendicular?