Minecraft wiki entry for Minecarts, associated text: Minecarts move at 8 m/s at top speed on a straight track. On a diagonal track they move at 11.314 m/s = sqrt(2) * 8.
Minecarts move differently depending on their load.
A minecart with a player inside travels 309m from full speed, staying at full speed for 176m.
A fully loaded hopper or chest minecart travels 40m from full speed.
An empty hopper or chest minecart travels 165m from full speed.
A chest minecart carrying 320 items (5 stacks) travels 101m from full speed.
Activated powered rails, down slopes, and being pushed by players or mobs add momentum to a cart, increasing its speed.
A minecart with a player inside goes from stationary to full speed after about 13m of powered rail.
A player riding in a cart may add momentum by "pushing" it using the forward control.
A stretch of an unactivated powered rail of at least two blocks length brings a loaded cart at full speed to a complete halt.
A long stretch of rail or an up-slope reduces a cart's momentum and thus its speed, eventually stopping it unless the forward key is held throughout by a player riding the cart.
Minecarts "bounce" off of obstructions on the track. Running into a player, mob, or a stopped cart causes it to reverse direction, even on a powered track.