Two carts with masses of 4.54 kg and 3.26 kg move toward each other on a frictionless track
with speeds of 5.41 m/s and 4.00 m/s respectively. The carts stick together after colliding head-on. Find the final speed.
This is an example of an inelastic collision between the two carts so you can use the following equation, showing conservation of momentum:
m1v1 + m2v2 = (m1 + m2)v
Where m1 and v1 are the mass and velocity of cart 1, and m2 and v2 are the mass and velocity of cart 2 before they collide, and v is the velocity after the collision.
Remember also that velocity is a vector, with magnitude and direction, so you have to decide which cart is moving in a positive direction.
Let's assume the 4.54 kg cart of velocity 5.41 m/s is moving in a positive direction to the right, while the 3.26 kg cart is moving in a negative direction to the left.
Using the above equation you get:
4.54 kg * 5.41 m/s + 3.26 kg * (-4 m/s) = 7.8 kg * v
Solve for v= + 1.48 m/s so the two carts are moving to the right.