proof help needed!?

Question

suppose g: (a,b) ->R^n is a twice-differentiable parameterized curve. prove that g has constant speed if and only if the velocity and acceleration vectors are orthogonal at every t.

any help on how to approach and solve this question will be much appreciated.

Answer 1

Assume g has constant speed. Then v.v is constant. This means 0=d(v.v)/dt=2*v.a where a is the acceleration vector. Hence v.a=0 so v and a are orthogonal everywhere.