The replies here are okay, but they actually just slightly miss the point of what is happening in the scene and how your camera is processing it. The d7000 is still on the older autofocus platform, but the one setting you can change is "focus tracking with lock on" and reduce it to the shortest time possible.

For this situation you shouldn't be using af-s at all so I will just stop talking about that.

You should be in af-c dynamic mode instead of single, and the reason why you need to reduce focus tracking with lock on is so that the camera will refocus as soon as it detects a change in distance to the camera. Without getting too technical, the camera remembers the distance the focus is at for a period of time before refocusing in case someone runs in front of the camera or if someone moves slightly out of the way of the focus point so you don't lose them. If you lower that setting, your camera will autofocus faster and will respond better to people moving back and forth perpendicular to the plane of focus of the camera.

Switching to dynamic will give you better results as well because more points will be used.

Just as an aside, you'll get the best autofocus performance out of the d7000 if you lower the number of focus points available and lower the number of focus points used in dynamic continuous autofocus.

Hope that helps. Let me know if you have any more questions. Someone else did mention it but back button focusing will be another tool that will help you. Someone also mentioned 3D and that is a good option as well but the focus tracking timing is your main issue and that will alleviate most of your problems by default.