A 1,600 kg train car rolling freely on level track at 16 m/s bumps into a 1.0 × 10^3 kg train car moving at 10.0 m/s in the same direction, and the two latch onto each other and continue together. What is their final speed?
Can someone give me the formula for this and maybe help with the steps?
I am totally confused over this one.

Question

A 1,600 kg train car rolling freely on level track at 16 m/s bumps into a 1.0 × 10^3 kg train car moving at 10.0 m/s in the same direction, and the two latch onto each other and continue together. What is their final speed? 
Can someone give me the formula for this and maybe help with the steps?
I am totally confused over this one.

frogbull2000 · Answer

That is supposed to be 1.0 x 10^3 kg

frogbull2000 · Answer

I know the answer of 14 m/s, but I don't know how to get the answer

jfraser · Answer

this is a conservation of momentum problem

jfraser · Answer

$$\Sigma (m*v_i) = \Sigma (m*v_f)$$

snowsurf · Answer

This will be using conservation of momentum. Let define initial momentum as p1i=mi1vi1 for first car and second car p2i=mi2vi2. Final p1f=mf1vf1 and p2f=mf2vf2.

Setup up the equation.
mi1vi1 + mi2vi2 = mf1vf1 + mf2vf2
$$\frac{ mi1vi1 + mi2vi2}{ (mf1 + mf2) }=v$$ Since the collide both cars will stick together and they will share the same velocity. Use this expression and you will find final velocity.