Question

why does the unit of time enter twice in the unit of acceleration?

Answer 1

Because acceleration is acquired through integration of velocity, in which it appears once. A velocity is given e.g. 5 meters per second. An acceleration is the change in velocity over time: e.g. 5 meters per second per second = 5 m/s^2. Meaning that your velocity increases by 5 m/s every second!

Answer 2

the unit of acceleration is the rate of change of velocity \[\frac{d}{ds}[\frac{m}{s}]=\frac{m}{s^{2}}\]

Answer 3

Thats what I was trying to express informally :D.