Hey guys,

I am just getting back into the realm of equations again, and have a question, that maybe someone more into the depths of this could help me with.

I am trying to find a formula, into which I input desired **Distance (s)** and** Time (t)**, resulting in a given **Initial Velocity (u)** in relation to a negative ** Acceleration (-a)**, so that *after* going the given **Distance (s)**, the **Final Velocity (v) = 0**.

What equations I think should help me achieve this somehow:

s = 1/2 * a * t^2 + (u * t)

v = u + a*t

**OR** in this case:

s = 1/2 * -a * t^2 + (u * t)

v = u - a*t

I know that as an example, if I wanted to go the **Distance (s)** __= 100m__ in **Time (t)**__ = 10s__, I would use the following values:

**1.)*** 0 = 20 - 2*10 [v = u - a*t]*

**2.)** __100m__ = -1 * 10^2 + (20 * 10) [s = 1/2 -a * t^2 + (u * t)]

**3.)** Now I could just increase the *Time (t)* as I want in relation to changing either the *Initial Velocity (u)* or *Acceleration(a)*; For example, if I wanted the **Distance(s) = 1000m**, I could change **Time(t) = 100**, and **Acceleration(a) = 0.2** .

But I struggle converting this knowledge and the relativity of the values to each other into a formula. I would grealty appreciate if anyone could help me out here.

Thanks for Your time.