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Hello, I am pretty new to the DSLR world. I own the cannon rebel t3i and love it so far. The lense it came with however doesn't suit what I'm trying to do. I'm trying to photograph auto racing. The lense I have doesn't have nearly enough zoom to acclompish this. This is all outdoors and is usually in the light. Can anyone give me some ideas on what I should be looking for? Should I jost go after a 300mm lense, or is there something else I should be considering as well?

I should also mention I'm trying to keep my budget around $300 since I'm a beginner.

hi and welcome.
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As for your choice of lens, auto racing needs a fairly long lens. the 300 you mention will be a good start, but if you continue, it will be just a start.But good quality fast lenses are usually expensive. As you mention, lighting is usually pretty good, so you don't need a fast lens. This will keep the price down somewhat.
Some examples: the Canon 200 f/2.8 is $755. The Canon 300 f/2.8 is $6388 while the 300 f/4 is "only" $1300. note that these are all out of your price bracket. You might consider second had lenses. There are some good bargains to be had with older stock, especially manual focus lenses. Also consider that with these long lenses, you will need a support of some kind to keep the image from shaking. A monopod is what most people use for racing.

Part of getting a good photo is technique. This is much cheaper than lenses as it only costs practice. Try getting to the track early and picking a good position where there is likely to be some action. Select where there cars will be when you take the photo, prefocus and wait for the car to come to you. when it does, you stand a greater chance of getting that magic photo, and if you choose your spot carefully, you may not need such a long lens.

Another thing. You mention a big zoom, then talk about a 300mm lens. A zoom is a different beast. A zoom lens allows you to change focal lengths without changing the lens. You might consider for example a 70 - 300mm lens. A telephoto lens has a fixed length, greater than 50mm and is usually better optically than a zoom at any given price point. This is because zooms are more complicated to make. You can f course have a zoom telephoto. The 70-300 would be one of these, but a "big" zoom refers to its zoom range, not its longest length. An 18-200 is a big zoom. A 70-200 is not.

Finally, check out the racing photos on this forum. There are plenty. Have a look at the EXIF data for the photos you like. This will tell you what lens and focal length was used, and will give you a better insight into the lens you need. Ask again if you need to find out about EXIF, but briefly it is information captured by the camera at the time the photo was taken. It includes time, date and possibly location. It also includes information about the camera used and the conditions: lens, focal length, aperture, shutter speed, ISO, White balance, flash etc etc