The other day while I was walking in the same direction that the train was accelerating. Then I came across this question. Please if would answer it, I am very curious to know. But when I walked the opposite direction as the train was accelerating, then it was easier.
I think the op asked a great question and did specify acceleration although I don't think that matters. There have been studies with treadmills and it has been proven that it's easier than running on the ground. You don't have to do any work to maintain forward momentum because the treadmill is coming toward you. On the other hand if a train was moving forward away from you, you would have to work even harder than walking on the ground to maintain. Part of your energy is used vertically moving up-and-down but it's the horizontal motion that makes a difference in what the OP is asking.
When you are standing in a train and it accelerates, your own inertia tries to fight against this acceleration. In order to keep yourself from sliding to the back of the train - to keep yourself motionless w.r.t. the train - you brace yourself against the floor and use your muscles to absorb the effects of the acceleration that is passed to you. Remember, when you walk, your legs are repeatedly pushing off against the ground, accelerating your body forward each step you take and then you slow back down between steps. So standing still on an accelerating train is, to your legs, like you are continuously stepping forward with that amount of acceleration. Hopefully, everyone follows me so far.
Now, say you want to actually walk in the same direction as the acceleration. In addition to the acceleration they are already providing (the amount that ensures your velocity matches the train's), your legs must provide extra acceleration in the same direction. If you want to walk the reverse direction, you can accomplish that to some extent merely by allowing your legs to relax and not match the train's acceleration. Then your own inertia will cause you to tend towards the rear of the train, which would make it seem easier to move in that direction.
The result? This would be equivalent to you standing on a slight incline or a hill (note that the equivalence principle of general relativity says that this is, in fact, exactly equivalent to standing on a hill); it's harder to walk up the hill (with the train) than down the hill.
The take home message is that things hate accelerating. When something like a train accelerates around us, we have to work harder to make our bodies keep up with that acceleration and even harder to overtake it, otherwise the floor of the train would simply move from under us and we'd slide to the rear.
In an accelerating train you are in a non-inertial frame of reference. You experience a fictitious force that appears to be pulling you in the opposite direction to the train's acceleration.
When this fictitious force is combined with the downward pull of gravity (which is actually another fictitious force but let's not go into that) the net effect is that walking in the direction of the train's acceleration feels like walking uphill; walking in the opposite direction feels like walking downhill.
The fictitious force can be observed in other ways too. A marble on the train's floor will roll "downhill"; a plumb line will not be perpendicular to the train's floor; and the water level in a cup will not be parallel to the train's floor.
Actually - acceleration of the train is not necessary - as long as it is moving, your kinetic energy is affected by the trains motion, because:-
Kinetic energy (E) is how much energy is needed to get an a object of some mass (m) moving. The mathematical formula relates to the velocity(v, or speed) squared. It takes 4 times as much energy to makes something move twice as fast.
So - if you were walking in the direction of the moving train, you're adding to your own existing kinetic energy (you're already on the moving train, so your already have same kinetic energy), so it's a lot harder than you expect (depending on the speed of the train - the slower, the harder!), while if you walk the other way, you're subtracting from your kinetic energy (the opposite), so you will notice a marked difference if you compare "forwards" and "backwards" on the same train.
Next time you're on a slow-moving train, try it out and see!