motion in a straight line

the distance covered d is proportional to the square of the time t ,so d=kt^2 ; k is a constant

the acceleration a is the second derivative of the distance covered with respect to the time, so a=2k

therefore, the acceleration is constant

$s=ut+\frac{1}{2}at^2$
$\Rightarrow kt^2=ut + \frac{1}{2}at^2$
$\Rightarrow 2kt^2=2ut+at^2$
$\Rightarrow 2kt=2u+at$
$\Rightarrow \frac{2kt-2u}{t}=a$
For any given instant, value of u and t are constant. So, a is constant.