# A person is pushed forward in a bus when brakes are out because of inertia or pseudoforce?

When a bus moving uniformly and suddenly brakes are applied, the person will be pushed forward. The explanation given in textbooks is inertia but cannot it be explained by the concept of pseudoforce as well? Say the bus decelerated with a, then the man of mass m will feel a pseudoforce ma forwards. This pseudoforce is what pushed him forwards.

Yes, that is just two ways of saying the same thing. The different descriptions stem from using different reference frames. The pseudo force (I prefer the term "inertial force") is simply inertia in a non-inertial frame.

Be careful because there is an illusion taking place here.

When the bus brakes, then the person is not being pushed forwards. Rather, the bus is being pulled backwards by a friction force - the person just continues moving forwards with unaltered speed.

Or at least, this is how a physicist would think about it in an inertial frame of reference. An inertial frame is a non-accelerating frame, such as how it looks from a person standing on the ground.

You could also consider this in the bus frame which is an accelerating frame. Meaning, as a person sitting in the bus. From the perspective of this person, when the bus brakes, the bus looks stationary. It looks as though the bus remains unaltered, while the person is being pushed forwards by some imagined force. This force does not exist in an inertial frame (of this reason, some people would say that it doesn't exist in reality), but in this accelerated frame it seems to exist. We call such imagined force a pseudo force.

Note that you can solve the scenario in either frame. It shouldn't matter for the result. But also note, that the backwards force on the bus and the pseudo force on the person do not appear at the same time in any of these two frames.

• @ Steeven Regarding your final comment. An observer in a non-inertial frame that was decelerating at approximately half the rate of the bus would observe the bus accelerate backwards and the passenger accelerate forwards. So they could assume both a backwards force on the bus and a forwards force on the passsenger, acting simultaneously. So "[a] backwards force on the bus and [a]pseudo force on the person" can be seen at the same time in some frames. Commented Jun 10 at 21:26
• @Penguino It is not true that "[a] backwards force on the bus and [a]pseudo force on the person" can be seen at the same time in some frames. You are just using two reference frames, thinking you are using only one. A connected confusion is also present in this answer because from the initial statements, one could conclude that " a person is pushed forwards or the bus is being pulled backward" have a meaning independent of the reference frame. Only after a few statements the importance of identifying the correct reference frame is stressed. Commented Jun 10 at 21:52
• @Penguino Thanks for the comment. I agree, and have edited the answer - I meant in any of the two frames that I have described, not in any frame entirely, so I miswrote. Commented Jun 10 at 22:10
• @GiorgioP-DoomsdayClockIsAt-90 I believe, of pedagogical reasons at this level, that my formulation is appropriate and is more aiding than confusing. But I appreciate the concern. Commented Jun 10 at 22:13
• Consider a bus A, with an unconstrained passenger B, that decelerates at 10 m/s^2 relative to the earth. A stationary observer C standing on the footpath, will observe A decelerate at 10 m/s^2 and will not see B decelerate. A second observer D, constrained to the bus, will observe no change of motion for A, but will see B 'accelerate' at 10 m/s^2. A third observer E, constrained in a car decelerating at 5 m/s^2 alongside the bus, will observe A decelerating at 5 m/s^2, and B accelerating at 5 m/s^2. Thus in E's non-inertial frame one can simultaneously observe two opposing "pseudo-forces". Commented Jun 10 at 22:18

A pseudoforce alone can explain the motion of the man, but only from one very particular reference frame - the non-inertial, accelerating reference frame of the bus itself. The pseudoforce only exists in an accelerating frame of reference, and the pseudoforce that is wholly responsible for motion only exists in exactly one frame of reference. You could say the man moves "because" of the pseudoforce, but only if you view the problem in this one very specific way.

It's often easier and preferable to describe the scenario in a non-accelerating inertial frame, of which there are an infinite number of equivalent choices. In any and all of these frames, the pseudoforce doesn't even exist - the man moves forward because the bus decelerates and he does not. There are an infinite number of reference frames where the pseudoforce doesn't exist, and a non-existent force can't be responsible for anything.

It always strikes me as odd to suggest that a pseudoforce can be the real underlying "cause" of anything, as its magnitude, direction, and very existence depend entirely on the wholly arbitrary choice of reference frame. Psuedoforces are not related to any underlying physical phenomenon like gravity or electrostatic forces, and are just bookkeeping tools that correct for non-inertial frames.

It's a bit strange to say a pseudoforce was the cause of the man accelerating forward, when not all observers even agree if there is a pseudoforce. An infinite number of observers in an infinite number of distinct inertial frames would agree that there is no pseudoforce in the first place, while exactly one observer in the particular frame of the bus would say the man's motion is due to the psuedoforce alone. I always find pseudoforces to be an unconvincing "cause", since pseudoforces have nothing to do with the behavior of the universe and its physical laws, and are wholly determined by your point of view.

Note that it's always possible to describe an accelerating system as being at rest, and subject to pseudoforces, which may not be terribly useful. If asked why an apple falls from a tree, the logical answer is "gravity" - not "the apple didn't fall from the tree, a cosmic-scale pseduoforce unrelated to any law of nature accelerated the entire planet upward to meet the unmoving apple" (even though both views account for the observed motion equally well).

When a bus moving uniformly and suddenly brakes are applied, the person will be pushed forward.

The person isn't "pushed" forward. The person tends to move forward with the velocity it had immediately prior to the onset of braking due to the person's inertia. Per Newton's 1st law an object moving at constant speed in a straight line will continue to move at constant speed in a straight line unless acted upon by an external force.

The explanation given in textbooks is inertia but cannot it be explained by the concept of pseudoforce as well

So called inertial "forces" are pseudo, or fictitious, forces. Another example is the centrifugal force, the apparent force that a person would attribute to feeling being pushed to one side of the bus when the bus is cornering. In terms of Newton's 1st law it is the person's inertia resisting a change in the persons direction that causes the person to move to the side.

Hope this helps.