Speed and Distance: Calculating Impact Velocity

[HellRaiser30]

I got a problem and it is that i have an object traveling at a certain rate of speed then another object traveling at another rate of speed hits it from behind to make the first object travel at a higher rate of speed and travel a certain distance from where it was hit till coming to a stop. If i know the distance the first object travelled, after being hit until it came to a stop, and how fast the first object was traveling at, before it got hit, is there an equation that will tell me how fast the second object must have had to been traveling at to hit the first object that distance?

 

[Astronuc]

One also asked:

There is one object at rest, then another object traveling at an unknown speed hits the first object causing it to accelerate to a certain speed and travel a certain distence until it comes to rest again, how do i find the unknown speed of the object that did the hitting if i know the speed that the first object accelerated to and the distance it moved.

Then what if the exact same thing happened but the object that was at rest and gets hit was already moving when it got hit and then comes to a rest.

is there a formula that i can use to find this out?

Well one has to have N equations for N unknowns. In physics, there are the laws of conservation of energy and conservation of momentum. But one must determine if the collisions are elastic or inelastic, and whether or not dissipative forces such as air-resistance or surface-to-surface friction are involved.

Please refer to these examples - http://hyperphysics.phy-astr.gsu.edu/hbase/colsta.html
http://hyperphysics.phy-astr.gsu.edu/hbase/inecol3.html