is it possible that an object moving in a certain direction with an acceleration in the perpendicular direction
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Yes , it is possible that and object moving in a certain direction with an acceleration in the perpendicular direction. Example : when a stone tied to a string is whirled in a circular path , the acceleration acting on it is always at right angle to the direction of motion of stone.
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Yes ,a body moving horizontally with an acceleration in vertical direction is possible in a projectile motion. Yes, for e.g. in a circular motion if one is moving with a constant speed, the motion is still said to be accelerated motion as the dirction of velocity changes at every point of the path.
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