How to generate a non-linear animation?

Here is a simple example, as time goes by, the speed of animation playback is increasing

The built-in function Animate seems to only play animation at a uniform speed, there is a related option DefaultDuration, I don’t know how to use it correctly

What is the simple way to create this kind of animation in Mathematica?

With[{tmax = 30},
 Animate[
   Graphics[
     {
       Black, Arrowheads[Large],
       Arrow[{{0, 0}, {t^3 + 10, 0}}]
     },
     PlotRange -> {{-20, tmax^3 + 10}, {-300, 300}},
     PlotRangePadding -> {Scaled[0.05], Scaled[.2]}
   ],
   {t, 1, tmax}
 ]
]