What informations I have:
- Distance to travel
- Initial speed
- Acceleration (constant)
What I need:
- Time it will take to travel that distance in the given conditions.
What would be the formula that gives me that?
If this answer is correct, the formula for an initial speed of $0$ is:
$$\text{time} = \sqrt{\frac{2 \cdot \text{distance}}{\text{acceleration}}}$$
I can't determine the equivalent with a non-null initial speed.
The formula $d = v_0t+(at^2/2)$ is what you want. The variable $v_0$ is the initial speed.
Use the quadratic formula to solve for $t$.