Question

Why does (second)2 occur in the unit of acceleration

Answer 1

because formula of acceleration is
v= 1/2 * a * t * t.
when time is in squere the ans will be in sq

Answer 2

In order to maintain the equation we take second square in the unit of acceleration.
like an example;
v =u + at
where
v = m/s
u= m/s
a= m/s^-2
t = t
when multiplied a × t the units second is denoted by t. so second square means t^2
so. here
m/t^2 × t gives m/t or m/s
so the equation is balanced
v = u +at
m/s = m/s + m/s