This is actually pretty tough to answer because of many variables.
The formula to be used in this case is mass x velocity x time.
But we also have to take into account the number of people capable of using each mode of transportation. So the solutions that we come up with have to be divided by the number of people that each mode can transport.
We have to assume that the distance is the same for each trip. Let's just say 1 kilometer. We also have to make some assumptions about the mass of some vehicles, the number of people that can ride on a train, and the average speed at which each mode operates.
Hopefully, nobody cares if I use the metric system.
I am going to assume that a person weighs 70 kilos (about 150 pounds).
Mass = 70 kilos
Avg speed = 5 kph = 1.4 m / s
Time to travel 1 km = 720 sec
Energy = 70560 units
Ave mass of a bicycle = 10 kilos (the mass of my bike)
Avg speed of a bicycle = 25 kph = 5.6 m / s
(source: http://en.wikipedia.org/wiki/Bicycle_weight_and_po... )
Total mass with rider: 80 kg
Time to travel 1 km = 144 s
Energy = 64512 units
Avg speed = 200 kph = 56 m/s
Avg mass = 299,000 kg
Passenger total = 309 people (although it is unlikely it will be full)
Added mass from passengers = 21,000 kg
Total mass = 320,000 kg
Time to travel 1 km = 18
Energy = 1,044,000 units per person
Car with 5 passengers:
Avg speed of a car = 80 kmh = 22 m / s (total assumption, there are an abundance of possibilities depending on where you are)
Avg mass of a car = 1600 kg
(source: http://www.newrules.org/voice2004/factoids/index.h... )
Added mass of passengers = 350 kg
Total mass = 1950 kg
Time to travel 1 km = 45 s
Energy = 390,000 units per person
Avg mass =70 kg (assumption)
Avg speed = 40 kph = 11 m / s (assumption)
Total mass with passenger = 140 kg
Time to travel 1 km = 90 s
Energy = 138,600 units
Avg mass = 460 kg
Avg speed = 50 kmh = 14 m / s
(source: http://en.wikipedia.org/wiki/Horse )
Total mass with rider = 530 kg
Time to travel 1 km = 72 s
Energy = 534,240
So the answer is the bicycle.
Cool, I am glad that is over with.
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