Question

A cart of mass 340 g moving on a frictionless linear air track at an initial speed of 1.2 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision the first cart continues in its original direction at .66m/s.
a) what is the mass of the second cart?
b)What is its speed after impact?
c)What is the speed of the two-cart center of mass?

I know that in an elastic collsion momentum and energy is conserved. What would be the equation i would use for this problem? I can't figure out the equations for a) and b) but I think for
c) would I use V= (m_1* v_1 + m_2 *v_2)/(m1+m2)

Why are you looking for "the" equation? Why don't you just solve them from the conservation of momentum and energy?
on a) I would start with momentum. That will give you the final momentum of car two.
Then, use conservation of energy to get final energy of car two. Both of those will yield mass, and speed.
On c, conservation of momentum: the equation
totalmass*speedcm= m1v1 + m2v2
you are right.

Answer 1

m2=m1(v1i-v1f/v1f+v1i)

v2f=2m1/m1+m2 all multiplied by v1i

the second part to this doesnt matter bc v2i=0