**We know that,**

**\(Displacement\propto\,time^3\)** …….1

Now, **\(Velocity=\frac{Displacement}{Time}\)** …….2

From equations 1 and 2, we get,

**\(Velocity\propto\,time^2\)** …….3

Now, we also know that, **\(Acceleration =\frac{Change\,in\,velocity}{Time}\)** …….4

From equations 3 and 4, we get,

** \(Acceleration\propto\,time\) **

Since, acceleration is directly proportional with time, so it increases with time.

**Hence option A is correct.**