special relativity - Is there a formula that gives the position of an object depending on the time, but which doesn't allow the object to surpass the speed of light?

I have found these two formulas:

$v = at + v_0$

$x = \frac{1}{2}at^2 + v_0t + x_0$

• a is the acceleration


• v is the velocity



• x is the position


• t is the time


• $v_0$ is the initial velocity


• $x_0$ is the initial position

The problem is that with an acceleration of $10$ m.s$^{-2}$ (for example) the object would surpass the speed of light in $3 \times 10^7$ s = $11$ months and $11$ days, which should not be possible.

Is there some other formula that gives the position of an object depending on its acceleration and on the time, but which works and does not allow the speed of the object to surpass the speed of light?