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  1. If I am sitting inside a closed sphere (I can't see the outside), can't I feel when the sphere is at constant speed ? Can I feel when it is accelerating ? Why ?

  2. The defination of force given somewhere is " In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate." So in a closed system, with no gravity, air friction (and some similar things), if I hit something, what will happen ? Will it continue to acclearate ?

  3. [Crackpot question] When a ball is at rest, its velocity, acceleration, jerk, jolt (and other terms) are zero. But when I suddenly hit it, suddenly velocity is nonzero (it's position has changed), so is probably accelaration (velocity has changed), jerk (accelaration has changed) and so on. What's happening here ? Am I wrong ? What happens when I expand in taylor series (of the distance) from just the moment before hitting (everything is zero) to just after the hitting (Everything is probably not) ?

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1) This is one of Einstein's relativity statement. An observer in an inertial frame cannot tell whether he is in motion or at uniform velocity as both corresponds to a non- accelerating situation. You can't "feel" velocity or rest, but acceleration, because an acceleration is accompanied by a force which changes your state of inertia (equilibrium). It is only the change in inertia you could feel. So you could feel only the force.
2) If you hit something it will accelerate. But hitting is giving a force for a very small time interval (Impulse). The body will accelerate only up to the force is applied. Once the force is release, it's not accelerating, But it can't stop because of it's inertia. So it will exhibit a uniform motion forever.
3) As I mentioned earlier the acceleration occurs only for that instant of time for which the force is applied. Otherwise it's contradictory to Newton's law. (Think something accelerating even if force is zero!!!) So in order to expand Taylor series, you have to consider only the instant at which you have given the force. Not after or before.

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