would an object's motion continue to increase in space after applying force on it(ignore gravity)
To determine an object's motion, you have to find out the net force it received.
So for your question, you need to provide the complete information of the object, including the initial condition and all the force on it.
If an object has a net force acting on it then it will accelerate. Once you remove that net force it will stop accelerating and its velocity will remain constant. The velocity can be zero or non zero.
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