Acceleration Help

[Kitsune]

I am having a bit of trouble with a math problem. It is math from a long time ago and simply cannot remember. Trying to get a formula which I can plug numbers into, maybe even use as a spreadsheet

We have a straight chase with one object chasing another, both the same vector. Trying to find time for object two to catch object one

Object One has an initial velocity and an acceleration. Object Two also has an initial velocity and an acceleration.

Finally, there is a distance between them.

I realize that it going to involve square roots. I am also thinking it may be one of those two answer equations. I have had calculus but it has been over twenty years though since I used anything this complex.

If I can get a time, I can calculate distance traveled and velocity when the two objects encounter each other.

[Lusankya]

Hmm... let me see.

S1 = a/2t^2/2 + vt + A

S2 = A/2t^2/2 + Vt + B

where S1 = position of object 1, and S2 = position of object 2

v= initial velocity of object 1, V= initial velocity of object 2

a= acceleration of object 1, A= acceleration of object 2

Solving for S1=S2

a/2t^2 +vt + A = A/2t^2 + Vt + B

(a-A)/2t^2 + (v-V)t + (A-B) = 0

Solve for t using the quadratic formula.

... I think.

[Steel]

Hmm... let me see.

S1 = a/2t^2/2 + vt + A

S2 = A/2t^2/2 + Vt + B

where S1 = position of object 1, and S2 = position of object 2

v= initial velocity of object 1, V= initial velocity of object 2

a= acceleration of object 1, A= acceleration of object 2

Solving for S1=S2

a/2t^2 +vt + A = A/2t^2 + Vt + B

(a-A)/2t^2 + (v-V)t + (A-B) = 0

Solve for t using the quadratic formula.

... I think.

Aaargh you used A as both an intial position and acceleration.


if object 1 starts at p1 with velocity v1 and acceleration a1
and object 2 starts at p2 with velocity v2 and acceleration a2

then

0.5*(a1-a2)t^2 + (v1-v2)t + (p1-p2) = 0

plug in numbers

solve with quardatic formula

[Lusankya]

Aaargh you used A as both an intial position and acceleration.

Whoops. That was dumb of me. I can't believe I didn't notice they were the same letter. :S