Question

a 4.0-kg cart rolling east on a level, frictionless track at 14 m/s collides with a stationary 3.0-kg cart. After the collision, the 4.0-kg cart is still rolling east, now at a speed of 2.0 m/s. Was this collision elastic or inelastic?

Answer 1

Use conservation of momentum, which MUST happen, to get the final velocity of the 3 kg cart, v.
4*14 = 4*2 + 3 v
v = 16 (east)
Now add up the initial and final kinetic energies to see if the collision is elastic.
Initial KE = (1/2)4*(14)^2 = 392 J
Final KE = (1/2)4*2^2 + (1/2)3*16^2 = 392 J

So, the collision is elastic.