How would the initial speed of a cart launched up a ramp compare to the final speed of the cart down the ramp at the same position, with friction and without friction?
The motion of a cart up and down an inclined plain (a ramp) is an example of symmetry, if we ignore air resistance and friction. Without those two non-conservative forces, the motion up and down the ramp is very similar to free fall with a reduced gravitational acceleration. This was the essence of Galileo's experiments on gravitational motion.
Consequently, without friction or air resistance the cart will have the same speed coming down the ramp as it passes the points it went through going up the ramp.
With friction and air resistance, the motion will not be symetrical. Friction and air resistance will convert some of the mechanical energy of the system into thermal energy by heating the air, bearings, wheels, and ramp as it moves. Because mechanical energy is being lost, there is less energy that can be used to create speed.
Consequently, as the cart comes down the ramp it will have speeds that are slower than those at it goes up the ramp.