*Originally posted by Darrie*

**I think what you're saying isnt really true. You pretend like a set of objects could accelerate a smaller (ie less heavy) object more than just one object could. It's not true because this is (for what i know) just a case of no energy can be lost (I don't know the proper English term, but you know what i mean). Thus the larger object gives all his kinetic ene ...[text shortened]... arger so v² has to be bigger and so does |v|.
**

I'm sorry if i misinterpreted your statement.

That's not what I'm saying at all. Let me explain with a few simple scenarios and quick calculations...

**Trial #1: Two objects only**
m1 = 10 kg

m2 = 0.1 kg

v1i = 10 m/s

v2i = 0 m/s

v1f = 9.80 m/s

v2f = 19.80 m/s

**Trial #2: Three objects in series**
m1 = 10 kg

m2 = 1 kg

m3 = 0.1 kg

v1i = 10 m/s

v2i = 0 m/s

v3i = 0 m/s

v1f = 8.18 m/s

v2f = 18.18 m/s

and after m2 crashes into m3,

v2f = 14.88 m/s

v3f = 33.06 m/s

As you can see, in the first scenario the 0.1 kg object attains a velocity of 19.80 m/s, and in the second scenario the 0.1 kg object attains a velocity of 33.06 m/s. In order for the two-object scenario to produce the same final velocity for the 0.1 kg object as the three-object scenario, the 10 kg object needs to be moving at approximately 16.70 m/s initially. There is no way to produce the same final velocity for the 0.1 kg object in the two-object scenario by increasing the first object's mass alone (the maximum velocity of the 0.1 kg object after one collision will be twice the first object's initial velocity, independent of its mass).

The trade-off here is between (a) the first object's velocity; and (b) the number of stages (i.e. complexity and mass) of the system. I was just wondering if there's ever a situation where changing (a) is unfeasible and changing (b) is the only solution. Does anyone know any situations like that?