Question

Prove that if a particle moves along a curve at constantspeed, then the velocity vector is at all times perpendicularto the acceleration vector.

Answer 1

if |v| is constant, then v•v = |v|^2 is constant
d/dt (v•v) = v•v' + v'•v = 2v•v' = 0
so, since a = v', a•v=0
and a⊥v