This is a second answer, because it is the same as my first only different.
The video from the men who landed on the moon shows what some might think is a contradiction.
They move SLOWER in a much lower gravity. Shouldn't they be able to move FASTER, if they weighed less? They should be able to just zip around.
But here is the explanation.
Force equals mass times acceleration.
So, if a person stands up from siting, in say half a second, on earth, the human muscle applies a specific force for a given time to achieve the right acceleration. If more force is applied, there is more acceleration and the person gets up faster. If less force is applied, there is less acceleration. The person gets up slower.
If the person now wants to stand up from siting in the same time frame on the moon, the exact same force has to be applied for exactly the same time, to achieve the same acceleration. Same mass on the moon as on earth. But here is the problem. The person want to STOP standing up. The stopping is done by gravity. On earth, the stopping force is much greater than on the moon. In fact, on the moon, the person would 'stop' perhaps five meters in the air. Not quite what was intended.
So to just stand up, not jump up, a lot less force has to be applied. But the mass is the same, so the acceleration is less. If the acceleration is less, it takes longer to complete the movement.
Walking is the same. If you want to walk at the same speed on the moon as on earth, you have to accelerate equally. Since the mass is the same, you have to apply the same force. But gravity is not pulling you back down on the moon at the same rate as on earth. You don't come back down in the same time frame. That first step on the moon is a very long one. If you want to go the same distance on the first step, as you do on earth, you have to apply less force, so you do not accelerate as fast, nor achieve the same speed. You have to walk very slowly. You need to keep the acceleration low. Otherwise, you keep overshooting your mark.
If you want to move a box starting from rest with a constant acceleration a distance of five meters in exactly one minute, you need to accelerate it by a specific amount to get up to the correct speed in the correct time. Any less or greater the acceleration, and the time is different. To get that specific acceleration, you need a specific force. It does not matter if this is on Earth or on Mars. Now, however, you might want to STOP it. Inertia says it is going to keep on going. On Earth, you can count on gravity, and friction, to slow it down. On Mars, the gravity, and thus the friction, are three times less. All things considered, it will go three times further. You, not friction and gravity, need to stop it. Think of stopping your car on glare ice.
If you want to throw a ball at a specific speed, you need to give it a certain acceleration. If you are doing it manually, you have only so much time (while it is in your hand) to impart that speed. You need to give it enough delta v, acceleration, in a given time. Same force on Earth as it is on Mars, to get a specific ball going at a specific speed in a specific time. But on Mars, because of the gravity, the same ball traveling the same speed will go three times further. To get the ball the same distance as on earth, you throw it at one third the speed. You apply one third the force. Your arm moves one third as fast. Things go slow.
So on Mars, if you want to perform the exact same procedure through a given distance as on earth, you need to do it three times slower, and apply one third the force.
If you do things in the same time frame (same acceleration) as on earth, you need to apply exactly the same force as you do on earth. Mass is the same, acceleration is the same, time is the same, so the force is the same. But the gravitational constraints on such things as projectile height, distance, friction are three times less, and you end up with three times the effect.
So if John Carter wants to go at the same speed in the same time as on Earth, it takes the same effort to accelerate and decelerate. However, the equivalent effect is perhaps three times greater. If John Carter wants to perform the equivalent actions with the equivalent effects and results as on earth, he will go three times slower and will use one third the effort.
One area, however, where this will not be a factor is in swimming. Swimming is independent of gravity. It is all about moving a given mass (both swimmer and water) a given distance at a given speed. It will take exactly the same amount of force to swim the same distance at the same speed on Mars as it does on earth. If John Carter is a swimmer, he will need the same physique as an Earth swimmer.
That earthly visitor to Mars will think that the Martians are moving very, very slowly indeed.