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)**[u:2br9o2qx]= 100m[/u:2br9o2qx] in

**Time (t)**[u:2br9o2qx] = 10s[/u:2br9o2qx], I would use the following values:

**1.)**

*[u:2br9o2qx]0[/u:2br9o2qx] = 20 - 2*10 [v = u - a*t]*

**2.)**

*[u:2br9o2qx]100m[/u:2br9o2qx] = -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.