The distance travelled by an object moving along a straight line is directly proportional to the square of the time. Its acceleration

Explanation

Let x be the distance travelled in time t. Then,
`x prop t^(2)` (given)
`x = kt^(2)` (Here, k = constant of proportionality)
We know that velocity is given
`v = (dx)/(dt) = 2 kt`
and acceleration is given by
`a=(dv)/(dt)=2 k` (constant)
Thus, the body has uniform accelerated motion.