Question

why acceleration cannot be defined as rate of change of velocity with respect to distace

Answer 1

Compared to displacement and velocity, acceleration is like the angry, fire-breathing dragon of motion variables. It can be violent; some people are scared of it; and if it's big, it forces you to take notice. That feeling you get when you're sitting in a plane during take-off, or slamming on the brakes in a car, or turning a corner at a high speed in a go kart are all situations where you are accelerating.

Acceleration is the name we give to any process where the velocity changes. Since velocity is a speed and a direction, there are only two ways for you to accelerate: change your speed or change your direction—or change both.