Minecarts are rideable objects placed on minecart tracks that are used to carry items, move the player faster, move automatically over a long distance, and to ride roller coasters. Whee!
Minecarts can be destroyed and reverted to a carriable item, even while riding them.
Minecart Riding
The rideable minecart.
Basic Physics
Minecarts can be ridden by right-clicking them, but the player cannot move the minecart while inside of it so it must already be in motion when sat in for it to go anywhere.
The minecart physics have been noted to be very unrealistic. Once pushed downhill a minecart will gain speed at an increasing rate until it reaches a cap. It also moves significantly faster/farther when ridden by a player rather than when pushed empty. An example of this is riding a minecart after being pushed up/down a slope of one block after which it will travel around an amazing 78 blocks, though very slowly by the end. A player used to be able to rapidly re-enter the cart or add "boosters" on tracks to increase speed, but these bugs have been fixed.
Players riding minecarts are not able to move, but they can exit the minecart by right clicking it. It is also possible to interact with the environment while riding a cart, such as shooting a bow at enemies or laying down track in front of the minecart while it is moving.
When riding a falling minecart, landing will deal no damage.
Energy Conservation
Although the minecart has a maximum speed, it does not appear to have a maximum energy. One can create a slope upwards of a tested 60 blocks, and achieve further and further travel distances.
One unit of energy could be defined as the energy gained by a cart going down a one block slope, and lost by a cart when it goes up a one block slope. If a 45 degree downward slope is connected directly into an upward slope, an initial height of 60 blocks will result in a final height of 40 blocks, a loss of 20 units of energy. But if 20 sections of flat track are inserted between the slopes, the final height will be 35. This implies that one unit of energy is lost for every 4 sections of horizontal track traveled with an initial stored energy of between 60 and 40. At much lower speeds, much less energy is lost, implying that the energy lost is a percentage of the cart's current energy. The above gives about 0.5% energy loss per section of track. One implication of this is that more energy lost when the cart has more energy, so a gradual slope should allow you to travel much farther distances than a steep slope followed by a long flat section.
Anything in the way of the minecart will take it to a dead stop, including: blocks, items, mobs, and moving off of minecart tracks. When a mob touches a minecart they affect it in the same way a player would, i.e. minecarts in motion bounce away from mobs in the way of its motion and mobs that move up against a still cart will set it in motion.
Minecart Storage
Currently the minecart cannot store any items but it has been able to in the past and it is planned to be able to in the future. In the patch update that made minecarts rideable Notch said "Rideable minecarts, but you can’t open them yet", implying that there will be only one minecart that can both be ridden and store items.
The old minecart empty.
The old minecart half full.
The old minecart's item screen.