Direction of motion if there are two unequal opposite forces

[NoahCygnus]

If a particle is in the state of rest on the ground , and I apply a force such that it produces an acceleration 4.9 $\frac{m}{s^2}$ upward , will it move upward , considering there's gravitational acceleration 9.8 $\frac{m}{s^2}$ in the downward direction, or will it remain at rest?

 

[BvU]

If the force produces that acceleration, then it must move. But it takes a force of $(9.8 + 4.9)m$ Newton to do this with a mass $m$. Any force less than $mg$ and it doesn't move.

 

[NoahCygnus]

If the force produces that acceleration, then it must move. But it takes a force of $(9.8 + 4.9)m$ Newton to do this with a mass $m$. Any force less than $mg$ and it doesn't move.

So it takes a force which produces an acceleration greater than 9.8 m/s^2 in opposite direction to gravitational acceleration to move the body in upward direction?

 

[JoePhysics]

The net force on the object must be positive (upward direction) for it to start moving in that direction, if it was initially at rest. If the body were free falling (and thus subject exclusively to gravity), a momentary application of a net positive force will slow it down (reduce its speed) but won't make it instantaneously start going up. This is a common misconception; it is the velocity vector which tells you in which direction the body is moving, not the acceleration.

 

[BvU]

So it takes a force which produces an acceleration greater than 9.8 m/s^2 in opposite direction to gravitational acceleration to move the body in upward direction?

To keep an object in place in a gravitation field it takes a force $mg$ to produce no acceleration whatsoever. It just compensates the gravity force. As Joe says, it's the net force that causes the acceleration.