How can force exist without acceleration? From what I understand acceleration does not cause a force, but rather forces cause acceleration, so if I have a ball moving with CONSTANT velocity, that hits a wall, then the wall must apply a force to deflect the ball (I am assuming no force by the ball since it is moving with constant velocity), but where does the force by the wall come from? Also if the wall does not accelerate to cause the force, how would you calculate it?
 A: First of all, I have to correct your terminology: acceleration doesn't cause force or vice versa. Acceleration is proportional to force, meaning, if acceleration exists, a force exists too.
Force, in its most basic form, is defined as a change in momentum, and that's how Newton stated it
$F=\frac{dP}{dt}=\frac{d(mv)}{dt}=m\frac{dv}{dt}=ma$
The wall does not "stop" the ball, but a collision happens, and the collision between the wall and the ball just reflects the ball doing nothing to the wall because the mass of the wall is very high compared to the ball.
Theoretically, when the the ball hits the wall, it gets repelled back because the wall is much stronger than the ball. Macroscopically, the wall absorbs the hit of the ball, and vibrates, and the vibrations damp so fast because the wall is very rigid, and realistically you don't even notice the vibrations.
How do you calculate that? You have to solve the classical collision problem. The mass of the ball is M and the mass of the wall tends to infinity.
A: Best to consider a real physical wall as slightly elastic like a hard rubber material. Clearly the wall depresses slightly on impact and elastic forces build up quickly to repel the ball back out. The forces are real and the elastic deformations are easily seen in slow motion replay using high rate video recorders.
