Newton's first law says that an object remains at rest or moves at a constant motion if there is no external force. Why do some objects remain at rest, while the others move at constant motion?
Being at rest is a special case of *moving at constant velocity", namely moving at the constant velocity =0. In fact, you could leave out this part of the sentence without losing anything.
Alternatively you could say, that, if there is no force, the object is not accelerated (i.e. acceleration=0).
Just a note:
While Newton's laws are sometimes stated as you did, you need to realize that it is a bit of a lazy shorthand notation of the law. Two things need to be expanded on:
- The "force" is actually the total effective force, i.e. the (vector) sum of all external forces. Of course, if you apply two equal in magnitude forces acting in opposite directions, the object would not accelerate either.
- It is actually not the velocity that is constant, but the momentum (mass times velocity). Similarly, in the absence of a force, it is actually not the acceleration that is zero, but the time derivative of the momentum. However, this is only of relevance in cases where the mass changes (e.g. in rockets). If the mass is constant, you end up with the simple version of the law (constant velocity, zero acceleration).