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)##