how does change in velocity divided by change in time equal m/s^2? (m/s final - m/s initial / s finals and s initial ) = m/s^2?

The unit of velocity is m/s while the unit of time is s.
Hence, the unit of change in velocity (i.e. final velocity - initial velocity) is m/s,
and the unit of change in time (i.e. final time - initial time) is s.

The unit of (change in time ÷ change in time)
= (m/s) ÷ s
= (m/s) × (1/s)
= m/s²

a = (vf - vi)/(tf - ti)
Unit of (vf - vi) = m/s
Unit of (tf - ti) = s
So, a = (m/s)/s = m/s^2

You can say = 1/s (m/s final - m/s initial) when s tends to zero. Like taking the limit.

K