shoot over the fence with something like a 200mm or 300mm zoom.
Argh! No that would be a 200 or 300mm Telephoto!
Or perhaps a 200-300 'zoom' or more likely, a 55-200 or 55-300 zoom
Zoom merely being a lens of variable focal length, and available in ranges covering both wide angle and or telephoto ranges
Nikon DX 55-200's can be picked up on e-bay 2nd hand for under £100, 55-300;s for a couple of hundred.... fair wack given the price of the camera, but not exhorbitant as far as lenses go.
For cheap reach on the Nikon though..... M42 'infinity-correction' adaptor for about a tenner of the bay, you can then mount any of the 'old' M42 thread Manual Focus lenses of the last century, and these can be very good value for money.
Most will be 'Prime' or fixed focal length, ie not 'zoom' (hence comment above).
Cheapest reach for your cash? Probably a 135mm portrait lens. These were common short tele lenses in thier day, and there are an awful lot of them knocking about, and 'slower' ones dont command a lot of money.
I have a couple, and one within reach is a Hanimar 135 f3.5. this is not a very fast lens, but its still one stop faster than any of the zooms mentioned above, which are only f4.6 at the short end, and two stops slower f5.6 at the long end you are most interested in using.... You can pick up a lens like that for probably less than a tenner, and while its not a modern multi-coated lens, and wasn't even considered a 'great' lens in its day, on a cop sensor camera, using only the centre portion of the field of view, probably as good optically as a kit lens. Bit short, perhaps, but 135mm x 1.4 crop factor is equivilent of 190mm nb a full frame camera, which is only a noggin off the long end of my general purpose 70-210 zoom for 35mm film cameras, used for most track-sport photography a decade ago, and at far greater ranges over run-off area and gravel traps than you have at a Speedway....
For cheap reach, could be quite a lot of bang for your buck.
Want even more? Well, with M42 prime's; you are likely to find 300mm the next most popular long reach lens. Again, many knocking around, and all usually keenly priced. Often slightly slower max aperture, but slower ones likley to still be as fast as common AF kit Zoom's at the long end, around f5.6, and they are going to be uber cheap... spotted one a minute ago an f5.5... 16 hours ago, yet to reach £2! A faster F 4.6 in good nick ought not cost you more than £30 delivered to your door! Again, on a crop sensor, that's equivilent of a 400mm lens on a full-frame camera, and an AWFUL lot of reach... you can take almost full frame pictures of the moon with that.... come to think of it, I have!
Zoom lenses were less popular in M42 mount; people that bought M42 cameras generally chose them for the wide availability of reletively good value primes available; this means that they are often even cheaper, though in M42 fit, few were 'as good' as equivilent primes and usually not as 'fast'.. though still you ought to be able to get an f4.5/5.6 70-210mm for around the £20 mark...
Only bug-bear of using MF lens and adaptor on the Nikon, at least on mine, is the camera offers absolutely NO metering modes through the lens. This means using seperate hand held meter.... I got one not long back for under £3 off the bay! Or as I have done.... taking meter reading through the kit lens, noting the ISO, shutter and appature settings; selecting manual mode, and then setting that shutter and ISO on the camera and the aparture on the M42 lens when fitted, then adjusting from there.... It's fiddly, but it's not hard.
Anyway, that's cheap reach. And you can get an awful lot for under £30... that's 1/3 the way to an AF 55-200 kit lens... if you think you'd use it once you have it....