What happens to the acceleration from an initial force according to the law of inertia? Say we hit a golf ball with a club. Hitting the ball requires a force = m*a. According to the law of inertia, velocity should be constant, but how can that velocity be constant if we hit the golf ball with a force, resulting in an acceleration?
 A: By 'law of inertia' you mean Newton's first law, which says that an object will move with a constant velocity while no net force acts on it.
If a net force does act on an object, then it will change the object's velocity in accordance with Newton's second law, which says that if a constant force, F, is applied to an object of mass m, the resulting rate of change of the object's velocity will be given by f=m*a.
So when you throw a ball, or hit it with a club, you apply a force to it, which causes the ball's velocity to change. After you've hit or thrown the ball, then in real life the ball's velocity will not remain constant, because it will be affected by other forces such as air resistance and gravity. That said, in physics questions and exercises your will often see statements such as 'a ball moving with constant velocity' because the question is telling you to ignore complications, such as air resistance, in order to focus on some other aspect of the situation.
A: The Law of inertia, states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force.
In your case, you are acting with a force and thus its velocity will not be constant. You can check this with some kinematics!
A: In high school physics, the law of inertia states that a body moves with a constant velocity on a straight line or stays at rest if and only if the sum of all external forces acting on it is equal to 0. In your example, that sum is not 0. We have an external force from a club that is not compensated by any other external force. Moreover, we could find the ball's acceleration knowing the force with which the club act on it (from Newton's second law)
A: 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).
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:

*

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


*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.


*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.
A: There are a lot of factors to cover here , but i'll make it simple
1> When the golf ball is at rest , it is following the law of inertia , it continues to remain at rest unless a force hits it in this case a club .
2> When the club hits the golf ball , it pushes it with a certain force till the time it is in contact with the golf ball thereby giving it a acceleration .
This can be calculated by $ F= ma $ .
3> When the club is not in contact with the ball , the last terminal velocity which is reached by the golf ball is what it continues for the rest of its journey keeping in mind there is no external force ( friction ) .
The terminal velocity can be calculated by $v=u+at$
4> This therefore doesn't violated the law of inertia " An object stays in its state of motion unless there is an external forces.
A: Let's say you hit a golf ball on the surface of the moon.
During the time of the impact, the ball accelerates with $F=m a$ causing the speed to go from zero to some final value $v$. If the acceleration was constant (which it isn't for collisions), then $v = a \,\Delta t$, as you learned from high school physics.
The law of inertia does not apply here, because a force is present along the direction of motion.
But after the hit is over, $F=0$ and thus $a=0$ and indeed $v$ remains constant.
I am ignoring the moons gravity here for simplicity.
