Is it true that an object is accelerating if acceleration $a$ is non-zero?

Question

Is it true that an object is accelerating if a $\ne 0$ ?

Answer 1

Yes, assuming that $a$ is the second derivative of the displacement of the object, i.e. the acceleration. $a = 0$ is exactly equivalent to saying that the object is not accelerating, so the opposite also holds true, i.e. $a\neq 0 \iff \mathrm{object\ is \ accelerating}$.

Linguistic point: in everyday life, if $a<0$, we would say the object is decelerating, but negative acceleration is perfectly fine (and usually preferred over positive deceleration) in math/physics.

Answer 2

Acceleration is a vector so if the $a\neq 0$ in your question represents only the magnitude then yes, there is a non zero acceleration. But $a=0$ (assuming $a$ is the magnitude )might not mean that the acceleration is zero, there might be change in the direction.