How does the speed of the carts after the collision compare with the initial speed of the moving cart?

Question

One cart hits and sticks to a second cart. Make a diagram showing the carts before and after the collision. How does the speed of the carts after the collision compare with the initial speed of the moving cart? Explain and show please using physics terms.

Answer 1

m1v1 + m2v2 = m1v1 + m2v2    --> left side of equation is initial, right side is final.  m means mass, v means velocity

 

I'm assuming the second cart is stationary. So v2 initial = 0

 

Since after the collision, the two carts stick, we have one velocity for the two objects that we will call Vf.

 

So we get m1v1 initial = (m1+m2)vf

 

so vf = m1v1/(m1+m2)

 

In words, this means the initial velocity gets scaled by the ratio of the initial mass to the total mass of the two carts.