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A more correct sentence would be to write:
"Acceleration must EXIST when velocity changes. "
The second part is impossible, as acceleration is the time-derivative of velocity.
Well, let me explain to you... the correct definition of acceleration is :
So that means, imagine you are driving a car and then you have a curve in front of you. Imagine tha you do the curve with CONSTANT SPEED. Even with constant SPEED there's and acceleration because the correct definition of acceleration is the change in velocity divided by the change in time. Velocity did'nt change its magnitude (speed), but it changed the direction, because you have a curve. So acceleration exists.
But you said velocity can remain constant when acceleration changes. The correct should be "speed can remain constant with constant acceleration".
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i think you got that idea from rotational motion. acceleration is a vector quantity, so any change in the direction or the magnitude will result in change in acceleration. as Jow said, you can maintain a constant speed through a curve, but due to the change in direction, it'll result in a change in both acceleration and velocity. So, speed can remain constant though acceleration may change.