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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.

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    $\begingroup$ The premises aren't very accurate: its easy/hard to walk when the train is accelerating, not just moving. $\endgroup$ – AccidentalFourierTransform Mar 20 '16 at 22:11
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    $\begingroup$ Could you add some more details in the body of your question please? In which direction, as opposed to which other direction? $\endgroup$ – texnic Mar 20 '16 at 22:12
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    $\begingroup$ This isn't actually a physics question but rather a question of human biomechanics. If someone pulls a rug from under your feet, is it easier to stay upright if they pull it forward or backward? $\endgroup$ – lemon Mar 20 '16 at 23:07
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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.

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  • $\begingroup$ This answer is not correct. The correct answer is that it does depend on acceleration, and does NOT depend on speed. It is not harder or easier to walk forward in a train when the train is moving at a constant speed. It is easier to run on a treadmill than on the ground, because you do not have to overcome air resistance on a treadmill. That has no relation to walking inside a train, where you DO have to overcome air resistance. $\endgroup$ – fishinear Feb 8 at 14:22
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Due to inertia. When the train accelerate, and if you are just standing inside the train, you tend to fall backward. Due to that tendency to fall backward, it is easier to walk in the direction of that tendency and hard to walk in opposite direction to the tendency.

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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.

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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.

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Actually - acceleration of the train is not necessary - as long as it is moving, your kinetic energy is affected by the trains motion, because:-

E=1/2 mv2

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!

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    $\begingroup$ Kinetic energy isn't the energy to "get an object moving", it is the energy a moving object has. $\endgroup$ – Kyle Kanos Mar 1 '19 at 13:40
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    $\begingroup$ Relativity says this is wrong. If you are on the train, you can always assume the velocity is zero before it started accelerating. Your previous kinetic energy relative to some other frame of reference is irrelevant $\endgroup$ – Jim Mar 1 '19 at 14:04
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    $\begingroup$ If this were true (in the absence of acceleration) then it would be easier to walk east than to walk west ! $\endgroup$ – gandalf61 Mar 1 '19 at 16:57
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    $\begingroup$ This is nonsense, theory says it's impossible to tell if you're on a train moving at a constant speed of 100kph, on a train that's not moving at all, or on a train that's moving in reverse at 100kph (ignoring noise, vibration, and the scenery rushing past). Any physics experiment done on each train will have identical results. $\endgroup$ – Nuclear Wang Mar 1 '19 at 17:16
  • $\begingroup$ OK you naysayers - the train is 1m/s (walking pace), you weigh 70kg, you step off (from a side-mounted gangplank) onto a treadmill generator. step in the opposite direction to the train, 1-1=zero velocity=0 energy on treadmill. step sideways (neither with or against the train, and your kinetic energy is E=.5mv^2 as treadmill slows you to rest, which is 70kg/2 1m/s^2 which is 35 joules. Step *with the direction of the train, 1+1=2m/s velocity, so, squared is 4. E=120 joules. How did you lose 35 walking one way, but gain 103 the other, if it wasn't harder to take the step? $\endgroup$ – Anon Coward Mar 3 '19 at 1:01

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