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A small trial-carriage is on a big trial-carriage.An observer A stands next to the trial in an inactive frame of reference.An observer B is sitting on the big trial-carriage. Now the big carriage is accelerated.

An example would be that we stand in the subway as an observer B, while A is staying on the platform and the small carriage is a skateboard in the subway.

What happens?

Right! The small carriage doesn't accelerate.For observer A it rests as long as the big carriage under it has moved away, then it falls down. There's no accerlation force that impacts it. In contrast observer B notices the small carriage moving backwards and suggests an acceleration force F. If he wants to he can messure it with a force meter. It is a force called inert force that is caused by the carriage's inertia. In the inactive system of A this force does not appear.

We know:

inert forces only appear in an accelerated frame of reference.