If the displacement of an object is proportional to the square of time, then the object is moving with:
$(a)$. uniform velocity
$(b)$. uniform acceleration
$(c)$. increasing acceleration
$(d)$. decreasing acceleration

As we know the second equation of motion, $s=ut+\frac{1}{2}at^2$

Here, $s\rightarrow$ displacement

$u\rightarrow$ initial velocity

$a\rightarrow$ acceleration

$t\rightarrow$ time

If the displacement of an object is proportional to the square of time, then the object moves with uniform accelerated motion.

Therefore, option (b) is correct.