Why is acceleration measured in meters / seconds squared?

is calculated by dividing change in velocity by time. Since velocity can be measured in m/s and time can be measured in s the unit is meter/sec/sec or meters/##s^(2)##.
Let’s say you speed up from 10 m/s to 25 m/s and it takes you 5 seconds to do that. Acceleration is (##v_f## – ##v_i##)/time.
##v_f## = 25 m/s
##v_i## = 10 ms
t = 5 s
acceleration = (25 m/s -10 m/s)/5 sec
= (15 m/s)/ 5 sec
= 3 m/s/s or 3 m/##s^(2)##