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While i am standing in a bus that is accelerating an inertial force is acting on me in the direction opposite of acceleration (I understand that). But, what is the magnitude of that force.I thought it has the same value as the force that acts on the bus causing it to accelerate, but if it was the same value then my acceleration would be huge ( because my mass much lower than the mass of the bus). Can someone help, seems like there is a flaw in my thinking?

Edit: SmarthBansal pointed out that the force acting on me is equal to the mass*(acceleration of the bus). I still dont understand how do i then stay in the same place just by holding on the bar? (thanks)

Milan
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While i am standing in a bus that is accelerating an inertial force is acting on me in the direction opposite of acceleration (I understand that).

The important bit here s not that you're on an accelerating bus, but that you're imagining yourself to be at rest relative to the bus and using the bus as your reference frame. Once the bus accelerates, the reference frame of the bus is now non-inertial.

People on the sidewalk watching you see that there's no force pushing you backward, that's just your interpretation on the bus.

But, what is the magnitude of that force. I thought it has the same value as the force that acts on the bus causing it to accelerate.

In this case what is equal is not the force, but the acceleration. As the bus moves forward in the inertial frame with acceleration $a$, you experience in that non-inertial frame a force that would tend to move you backward with acceleration $a$ as well. Smaller masses experience smaller "forces".

The bus acceleration won't be terribly quick to move (both because it is big, and to keep from toppling standing passengers). Probably less than $\frac g3$. So friction on your feet and your grip on the bar are quite sufficient to overcome this inertial force and allow you to stay on your spot on the accelerating bus.

BowlOfRed
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You and the bus just feel the force that your mass generates inside the bus. If you felt the same force that accelerates the bus, it would not move because the net force is zero.

Metalbeard
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