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Physics question

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Position? doesn't make sense.

If you mean velocity, then yes. When you throw a ball in the air, the acceleration is constant, but it is briefly at zero velocity.
 
An object can have quite high angular acceleration and simply be rotating in place as well. TuxDave has the most encompansing answer and danfungus is correct.

edit...

editing out responses to things which were edited out.
 
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