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.