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Q. If the net force acting on an object is in the positive x-direction, the object moves only in the positive x-direction.

It is not true, the object will accelerate only in the x-direction, but it may be traveling in the y-direction and it could continue to do so making the path it follows a parabola. Think about a ball kicked off a cliff. There is a net force only in the y-direction (gravity) so the ball will accelerate downwards while continuing with a constant horizontal velocity.

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