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Edit in order to address questions in comments:

Anna I am not sure I understand you, but let me try answering. First of all, force is a vector, and Fnet is the vector sum of all forces which on being equal to zero will result in zero acceleration of the object of interest. Now let us simplify things by restricting forces to be in one dimension-you add or subtract depending on whether the force acts along the +x direction or the -x dir ( which dir is positive and which is negative is just a matter of convention). When you say "F-mg" you mean that there are 2 opposing forces on the object of interest, and the resultant will be the net force on the object, and it accelerates (during the interval in which it experiences the force) with a=Fnet/m, where m is the mass of the body/object. Now, if there is only one force acting on the object, the net force will be equal to that force and the object accelerates. I don't see why there should be another force for it to move. But surely, it needs an equal and opposite force if you need the net force on the object to be 0.

Also, I don't know what you mean by force getting "used up". You need an net non zero force on the object to give it an acceleration. Perhaps I can say that the net force is used up in increasing the objects momentum. (if that can make you understand)

When you hit the ball with a golf club:

1. I don't understand your last sentence where you say the force F should go to zero with time

2. while hitting, say you hit in a way that the ball moves horizontally on the ground and doesn't leave the ground. That is, you are giving it a horizontal force, and friction does oppose it. If there were no friction or other forces opposite to the direction in which you apply force, the ball while in contact with the golf club would accelerate with a=F/m where F is the force you apply on the ball with mass m. However, since in reality there is friction, acceleration is lesser, it will now be Fnet/m, where Fnet =(F-f) where f is the frictional force.

3. Gravitational force will not act to accelerate the ball when your force is horizontal: gravity acts in the vertical direction and is balanced by the normal force on the ball by the ground, making the net vertical force=0( as is evident by the fact that the ball doesn't fly into air,leaving the ground). However, if the force F that you apply has a vertical component greater than the gravitational force ,it leaves the ground, and you can then consider the gravitational force in your calculations of the net vertical force.(net force in the vertical direction= vertical component of your force - mg).

Keep in mind that force is a vector quantity and you cannot add horizontal and vertical forces.

Now the ball has an acceleration whose vertical component depends on the net vertical force and the horizontal component depends on the net horizontal force.

First of all, the other two who have answered are right and please read the answers with care. The velocity of an object remains constant ONLY when there is NO NET FORCE acting on the object(Law of inertia). Hence you are wrong to think about the law of inertia when you hit the ball(i.e, apply force), aren't you?! If we go by your thinking, applying law of inertia everywhere, there will not be any motion/change in velocity of any object, isn't it? :) (Read the complete statement and understand it clearly before you apply it to situations)

"all the physics world problems say that a ball is thrown with a constant velocity but how can the velocity of a thrown ball have constant velocity and no acceleration if it requires a force to start it with F = ma?"

Now the sentence

"the ball is thrown with a constant velocity"

is not technically very clear and is probably the reason for your confusion. Whoever made that statement just means that the the ball is thrown to have a certain (final)velocity which is constant after it is thrown, and the problem that you are asked to solve refers to that interval after throwing and letting it free in which the ball has a certain constant velocity (unless you again apply force on it).

You are right, you need a force to start it. The ball accelerates from rest only in the interval during which the net force on it is non-zero (the interval in which you give it a push). Once it is left free after hitting/pushing, it no more experiences any force and travels with the velocity it gained during the acceleration("final velocity"). If you need to change its velocity, you need to apply a (net non-zero) force again.

(Try to think of these experiments in free space where there is no gravitational force/air resistance etc. If your imaginations are on the earth, you are sure to go wrong because the velocity of the ball after you leave it in free air will change due to gravity/air resistance).

First of all, the other two who have answered are right and please read the answers with care. The velocity of an object remains constant ONLY when there is NO NET FORCE acting on the object(Law of inertia). Hence you are wrong to think about the law of inertia when you hit the ball(i.e, apply force), aren't you?! If we go by your thinking, applying law of inertia everywhere, there will not be any motion/change in velocity of any object, isn't it? :) (Read the complete statement and understand it clearly before you apply it to situations)

"all the physics world problems say that a ball is thrown with a constant velocity but how can the velocity of a thrown ball have constant velocity and no acceleration if it requires a force to start it with F = ma?"

Now the sentence

"the ball is thrown with a constant velocity"

is not technically very clear and is probably the reason for your confusion. Whoever made that statement just means that the the ball is thrown to have a certain (final)velocity which is constant after it is thrown, and the problem that you are asked to solve refers to that interval after throwing and letting it free in which the ball has a certain constant velocity (unless you again apply force on it).

You are right, you need a force to start it. The ball accelerates from rest only in the interval during which the net force on it is non-zero (the interval in which you give it a push). Once it is left free after hitting/pushing, it no more experiences any force and travels with the velocity it gained during the acceleration("final velocity"). If you need to change its velocity, you need to apply a (net non-zero) force again.

(Try to think of these experiments in free space where there is no gravitational force/air resistance etc. If your imaginations are on the earth, you are sure to go wrong because the velocity of the ball after you leave it in free air will change due to gravity/air resistance).

First of all, the other two who have answered are right and please read the answers with care. The velocity of an object remains constant ONLY when there is NO NET FORCE acting on the object(Law of inertia). Hence you are wrong to think about the law of inertia when you hit the ball(i.e, apply force), aren't you?! If we go by your thinking, applying law of inertia everywhere, there will not be any motion/change in velocity of any object, isn't it? :) (Read the complete statement and understand it clearly before you apply it to situations)

"all the physics world problems say that a ball is thrown with a constant velocity but how can the velocity of a thrown ball have constant velocity and no acceleration if it requires a force to start it with F = ma?"

Now the sentence "the ball is thrown with a constant velocity" is not technically very clear and is probably the reason for your confusion. Whoever made that statement just means that the the ball is thrown to have a certain (final)velocity which is constant after it is thrown, and the problem that you are asked to solve refers to that interval after throwing and letting it free in which the ball has a certain constant velocity (unless you again apply force on it).

You are right, you need a force to start it. The ball accelerates from rest only in the interval during which the net force on it is non-zero (the interval in which you give it a push). Once it is left free after hitting/pushing, it no more experiences any force and travels with the velocity it gained during the acceleration("final velocity"). If you need to change its velocity, you need to apply a (net non-zero) force again.

(Try to think of these experiments in free space where there is no gravitational force/air resistance etc. If your imaginations are on the earth, you are sure to go wrong because the velocity of the ball after you leave it in free air will change due to gravity/air resistance).

First of all, the other two who have answered are right and please read the answers with care. The velocity of an object remains constant ONLY when there is NO NET FORCE acting on the object(Law of inertia). Hence you are wrong to think about the law of inertia when you hit the ball(i.e, apply force), aren't you?! If we go by your thinking, applying law of inertia everywhere, there will not be any motion/change in velocity of any object, isn't it? :) (Read the complete statement and understand it clearly before you apply it to situations)

"all the physics world problems say that a ball is thrown with a constant velocity but how can the velocity of a thrown ball have constant velocity and no acceleration if it requires a force to start it with F = ma?"

Now the sentence

"the ball is thrown with a constant velocity"

is not technically very clear and is probably the reason for your confusion. Whoever made that statement just means that the the ball is thrown to have a certain (final)velocity which is constant after it is thrown, and the problem that you are asked to solve refers to that interval after throwing and letting it free in which the ball has a certain constant velocity (unless you again apply force on it).

You are right, you need a force to start it. The ball accelerates from rest only in the interval during which the net force on it is non-zero (the interval in which you give it a push). Once it is left free after hitting/pushing, it no more experiences any force and travels with the velocity it gained during the acceleration("final velocity"). If you need to change its velocity, you need to apply a (net non-zero) force again.

(Try to think of these experiments in free space where there is no gravitational force/air resistance etc. If your imaginations are on the earth, you are sure to go wrong because the velocity of the ball after you leave it in free air will change due to gravity/air resistance).