Velocity/Acceleration equals Time

Assuming an object starts from rest, and has a constant acceleration, why is it that the velocity divided by the acceleration equals time?

I'll give you an answer without involving calculus given this exact rule isn't so most of the time, only when acceleration is constant. You'll want calc to solve for non-constant acceleration, so I'll assume you don't need or know calculus for this answer.

So yeah:
Acceleration is the change in velocity over a period of time.

Velocity is the change in displacement over a period of time.

You know that for constant velocity, displacement/time is the velocity, or v=d/t.

So it's analogous for acceleration and velocity. Given you're solving for constant acceleration, the velocity/time is acceleration, or a=v/t, thus, t=v/a.

acceleration is the change in velocity divided by the change in time. a= v/t hence with a little manipulation of the formula you can easily solve for time if given both the change in velocity and acceleration. t= v/a

Acceleration formula was originally derived from a Law.
The Law Of Rate Of Change Of Momentum.
It states that - a=P/2 ... (where P is Momentum)
Now P = v-u (final vel - initial vel)
Thus a = (v-u)/t
(and not just v/t...except for u=0)
...
:)