Question

why does the unit of time enter twice in the unit of accerlation

Answer 1

In terms of the physical definition of acceleration:
Acceleration is the change in velocity per unit time.
Velocity is the change in distance per unit time.
This would then extend to mean: Acceleration is the change in distance per unit time, per unit time. (We just apply the definition for velocity into the first definition).

We are twice considering time, so it is the unit: distance/time /time = distance/(time time) = distance/time^2

Answer 2

[a] = [v]/T = L/T/T = L/T^2