How to blur the background of a photo but keep subject focused? (image below)?

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like that?
my brother drives cars and does triathlons, and i'm the camera guy. He wants me to be able to take photos like the one above. I'm new to dslr photography and have had my camera (nikon d5100) for only a few months. I still only have the 18-55mm lens, but i'm soon going to get a 80-200mm lens second hand off a friend. I would like to know the shooting mode, shutter speed, ect. Some techniques/ tips on how to do it and also, do i need a tripod?

That's slow shutter speed, in regards to what that is google it and study up on the technique

I would suggest you read up on panning (following the subject with the camera).It can be done with a tripod and the right head, but I prefer freehand.

In some ways the 80-200mm can be a great lens. It lacks some things, which is why you plausibly could get one in very good condition at a good price. However, what it lacks may annoy you. It requires a camera with an autofocus motor (e.g. D7000, D90, D300) to autofocus.
It lacks VR, although the wide aperture can make that less important.
With some practice you can probably make the manual focus work for you. If you know where your brother is going to be, carefully compose and prefocus on that spot. When he is approaching, follow and pan, and hit the shutter when he gets to the spot that should be in focus.
I don't know if this lens is parfocal. Most zooms are not. If it is not parfocal then changing the zoom would alter the focus.
Unless your brother tends to be in first place, you can take practice shots on the cars, bikes, and runners ahead of him, so you will be well prepared when he arrives.

You could take panning shots like that with your 18-55… Just close down your aperture to F11 or so.