Why is it impossible to start or stop an object instantaneously? In what ways can a non-accelerating object move?

I think this has to do something with inertia, but I am not exactly sure I fully understand the concept.

For the second part, does this mean, like a book sitting on a table, but the world is still spinning, therefore, the book is changing direction and is then accelerating?

Any help would be appreciated!

  • 1
    $\begingroup$ Hint for question 1: how much acceleration would it take to instantaneously change the velocity of an object by a finite amount? Hint for question 2: acceleration is change in velocity. Consider the implications of acceleration being zero. $\endgroup$ – probably_someone Oct 7 '19 at 0:12
  • $\begingroup$ Define "instantaneously". And note - an electron exposed to an electric field accelerates at an EXTREME rate due to its very small mass and large charge/mass ratio. $\endgroup$ – David White Oct 7 '19 at 1:55

To move an object you must apply a force where $F = m\vec a\ and\ \vec a = d\vec v/dt$. To move it instantaneously implies that dt --> 0 and the force would go to infinity. Hence instantaneous acceleration or deceleration is impossible.

A non-accelerating object can only move with constant velocity in a perfectly straight line. Any curve in the line implies the object encounters a change in direction or a change in speed and either of these is an acceleration.

To an observer outside of earth, yes the book would be accelerating, but to an observer on earth, the book would be stationary. It depends on the reference frame.


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