We don't fall out of an elevator when it goes up or down at high speeds because of the principle of inertia and the force of gravity.
According to Newton's First Law of Motion, an object at rest or in motion will remain at rest or in uniform motion in a straight line unless acted upon by an external force. This principle is known as inertia. When the elevator accelerates upwards or downwards, our bodies tend to maintain their state of motion due to inertia.
Additionally, the force of gravity acts on our bodies, pulling us towards the Earth. As the elevator moves, the force of gravity continues to act vertically downward, keeping us in contact with the floor or the walls of the elevator.
So, even when the elevator accelerates upwards or downwards, the combination of inertia and the force of gravity ensures that we remain in contact with the elevator, preventing us from falling out.