If a ball is thrown upward with velocity of 1m/s, is vx = 0 while vy= 1?
Yes, assuming that the ball is thrown straight upwards and the y axis has been chosen to point straight up.
And now that you have the easy yes/no answer that you were looking for....
You could have chosen the x axis to point straight up, in which case vx would be 1 and vy would be zero.
Or you could have chosen both axes sloping in opposite directions at a 45-degree angle to the ground. In this case both vx and vy would be equal to √2/2 and there's nothing wrong with that choice except that it complicates the math for no good reason.
if i choose x axis to point straight up, does that mean ay= 0 and ax= -9.8m/s^2?
This is a 'confidence thing" I think. When you're a student and the teacher draws axes on the blackboard, everyone thinks "Why ever did she choose that set of axes?". The answer is pretty much always that they have found that they get the right answer to that problem quicker and easier that way.
There's a great example where you are dealing with objects on an inclined plane - do you use vertical and horizontal axes or do you use parallel and normal to the plane? It doesn't really matter but one way will turn out easier for some problems and the other will turn out better for others.
The only thing you need to remember is to keep rigidly with whatever convention you started with for the whole duration of your answer. The up/down thing can give you grief, too.
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