Calculus 8th Edition

Velocity vector $v(t)$ and acceleration vector $a(t)$ are orthogonal.
Tangential acceleration $a_T$ is zero because the particle moves with same speed. Let us consider $v(t)$ as velocity vector and $a(t)$ represents as acceleration vector. Use formula $a_T=\dfrac{v(t) \cdot v'(t)}{|v(t)|}$ When $a_T=0$ $\implies$ $v(t) \cdot v'(t)=0$ Hence, we can see that $v(t)$ is perpendicular to $v'(t)$ or, the terms velocity vector $v(t)$ and acceleration vector $a(t)$ are orthogonal.