Acceleration is a change of velocity. Velocity is a vector, in which both the
magnitude and the direction is relevant. If the direction changes, it is no longer
the same velocity. Equivalently, you can separate the velocity into an x-component
and a y-component (and a z-component, if the problem involves three dimensions).
Two velocities are considered to be equivalent only if all components are the same.
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Answer #1.5 :
One of the keys to answering the question is to point out that "acceleration"
does NOT mean "speeding up", which, unfortunately, is the way that virtually
everybody uses that word.
It may have all started when the auto industry decided to call the gas pedal the
'accelerator'. That's just my conjecture. I could be wrong.
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