newtonian mechanics - Force when acceleration is zero

i tried to find it in books but i was unable to do so and i am not able to understand this and I couldn't think of a better example. i repeat. its just an example. if i punch someone's face with my arm having constant velocity, it will mean that the acceleration of my arm is zero. F=ma, therefore force exerted by my arm is zero. Now if the force applied is zero the why does the person whom i punched experiences pain. please help. thanks.

Answer

For simplicity's sake, let's start with punching a concrete wall. Let's assume you are not strong enough to actually damage the wall. So (again for simplicities sake) if your fist is traveling at 1 m/s, when it hits the wall it will be moving zero, so it DECELERATES as part of the process of colliding with the wall, and the force of that deceleration will be applied to your hands (possibly breaking your knuckles). The mass of the wall is not relevant; this is why your hand would take the same damage from a smooth rock as it would from punching a large lead weight, it's just about the deceleration of your hand.

If you start slowing down your hand slightly before you punch the wall, your hand will have to do less deceleration when it collides, that's why your knuckle bones would be less broken. The same would be true if you were moving slower to begin with.

Now let's say you're trying to punch Neo from the Matrix. He sees you coming and dodges backwards, and coincidentally he happens to quickly accelerates enough (which takes energy from his muscles) so that he is moving his face backwards at the same speed that your fist is moving. Your fist will never actually hit him, so there will be no force applied to your hand.

Now let's say you're trying to punch the guy that stole your girlfriend. The same deceleration will occur. Some of the force from the deceleration of your fist at collision will go into breaking his jaw. Some of the force from the deceleration will go into moving his head back (if his head moves, your fist and his face receive less damage, because the force of your punch went into moving his head backwards). And some of the deceleration force will still go into hurting your hand.