Is it possible object moving with constant acceleration but zero velocity?
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The term acceleration implies that the velocity of an object is changing; inspite of that constant acceleration with zero velocity is IMPOSSIBLE.
When an object moves on A circular path, it's direction is along the tangent of the circle but the acceleration is towards the radius of the circle.
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When an object is thrown upwards, the maximum height velocity of the body is zero, but constant acceleration due to gravity is still working. The object can move in a certain path with a perpendicular acceleration, in the case of circular motion.
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