You left out part of the name of that lens....it's the Tamron 75-300
F4-5.6. That means that the maximum aperture is F4 (at 75mm) and F5.6 (at 300mm).
The maximum aperture is a rather important thing to consider, especially when choosing a lens for sports. Using a larger aperture will allow you to get a faster shutter speed...and a faster shutter speed is essential when you want to freeze the motion of a moving subject. Further to that, when shooting with the camera & lens in your hands, you will be subject to 'camera shake' which causes blur. The longer the lens, the more blur...and again, faster shutter speeds will help to alleviate the problem.
So when choosing a lens for sports, you will probably want to look at lenses that have a larger maximum aperture (lower F number). The problem is that these lenses tend to get rather expensive...especially when we're talking about long lenses with large max apertures. The average sideline photographer (for say football), is probably carrying around $10K to $15K worth of lenses.
You didn't mention a budget (but with a name like DR_Malibu, I recommended the most expensive options
)
There are more budget friendly options, of course. Canon, Tamron & Sigma all have a 70-200mm F2.8 that isn't all that expensive (compared to those other lenses). Canon also has a version with IS, the newest version of which, is rather expensive.
Of course, you can also get faster shutter speeds just by raising your ISO...but that also gives you more digital noise. And there is still a limit to ISO, so a larger aperture can still give you a faster shutter speed.
The key to all of this is light. If you are trying to shoot sports in low light situations...you are fighting a loosing battle. Better lenses and high ISO can help...but only to a point. But when you can shoot in great light, you may find that something with a max aperture of F4 to F5.6 might be perfectly OK.
And lastly, there is the quality of the lens to consider. I think that the Tamron 75-300mm is a fairly cheap lens, so it's likely that the image quality isn't top notch..especially at the long end of the zoom. Something like the Canon 70-300mm IS, is a higher quality lens....and I think they have a new 70-300mm
L lens, which should be very good.
