Conservation of Momentum, Question Regarding Force

[RoyalFlush100]

So I read that the conservation of momentum is a result of:
F1=-F2 <Newton's Third Law
t1=t2 <Time in contact
Therefore:
F1*t1=-F2*t2

F=m(Δv/t)
Ft=mΔv

So we can conclude:
m1Δv1=-m2Δv2
Therefore momentum is conserved.

Now what force is this? Would it be the same normal force that exists when an object is sitting on a surface? I don't think that would make sense, because normal force simply counteracts other forces (such as gravity) when objects are in contact, yet an object moving in inertia wouldn't have any applied force, so it wouldn't be counteracting anything. So then, what is this force that opposes objects' motion as a collision occurs between masses?

 

[Orodruin]

Now what force is this?

Any force between two objects.

because normal force simply counteracts other forces (such as gravity) when objects are in contact, yet an object moving in inertia wouldn't have any applied force, so it wouldn't be counteracting anything.

This is not true in general. You are probably thinking of a static situation.

 

[RoyalFlush100]

Any force between two objects.This is not true in general. You are probably thinking of a static situation.

So say a scenario like this exists:
Object A is moving at 10 m/s towards Object B, while Object B is moving at 15 m/s towards Object A. Both objects have a mass of 1 kg.
How do we know what each object's individual momentum will be then? All the questions I was given in class had some info about at least one of the objects both before and after impact.

Would it depend on how long the contact occurred for? Like this, say contact lasted for 2 seconds:
(10-15)/2=-2.5 Newtons of force on object A, meaning:
-2.5=1*a
a=-2.5 m/s^2
That's applied for 2 seconds:
-2.5*2=-5, meaning object A will slow down to 5 m/s (10-5=5)

 

[Dale]

Would it depend on how long the contact occurred for?

Yes, that is precisely one of the two reasons that seatbelts and airbags save lives.

 

[Orodruin]

How do we know what each object's individual momentum will be then?

You dont, not without more information. What you do know is that total momentum is conserved. You will have to look at the particular nature of the collision (eg, elastic, completely inelastic, etc) to draw more conclusions.