Railroad car a rolls at a certain speed and makes a perfectly elastic collision with car b of the same mass. after the collision, car a is observed to be at rest. how does the speed of car b compare with the initial speed of car a?

The speed of the car B after the collision is same as the speed of the car A before collision.

Explanation:

lets take the mass of the car A = m kg

Initial speed of the car A = u m/s

The mass of the car B = m  kg

Initial speed of the car A = 0 m/s

The final speed of the car A = 0 m/s

The final speed of the car B = v

There is no any external force on the masses that is why the linear momentum will be conserve.  

Initial linear momentum = Final linear momentum

P = mass  x velocity

m u + m x 0 = m x 0 +  m v

m u  + 0 = 0 + m v

m u = m v

v= u

Therefore we can say that ,the speed of the car B after the collision is same as the speed of the car A before collision.