All engines have power bands.
Generally these are vaguely S shaped.
What it means is that an engine produces a certain amount of power at a given RPM and that the power changes at a certain rate for a given increase in revs.
At slow revs the power increases slowly; this is the bottom part of the S. If you run in this area, not only do you have little power to keep going but the engine doesn't get mor powerful very quickly, so you don't accelerate very fast.
For the middle bit the power line may appear straight, that is for each gain in revs, the power goes up an equal amount. This is also the steepest part of the curve. In this area you will get most power to keep a certain speed and most acceleration if you put your foot down further. The steepest section is often known as 'the power band'.
At the top, the power created is less for the extra revs, it's like the bottom of the curve but in reverse. Eventually the power curve reaches a maximum and te engine cannot produce any more power.
In some engines, the revs may continue to rise but the amount of power produced begins to fall. This is the 'hook' at the top of the S. If you have a very long straight you may be able to use the revs at the top end, provided the power available is enough to overcome the drag of the kart, but in this area you aren't going to be accelerating as fast as you would in the power band.
Depending on the track design and your driving ability, you may find an advantage to gearing to use the high revs and carrying speed through the corners or you may find that there is an advantage in giving up some of the high end speed and use the acceleration through the corners.
The more teeth there are on the rear sprocket, the slower the kart will be able to go as a maximum speed, but the faster it will accelerate.
People sometimes get confused by the terminology.
A 10 sprocket on the front and a 60 on the rear is written as 10:60 and means the axle will turn once for every 6 revs of the engine. This means the kart will have a high top speed but low acceleration. It is sometimes also known as 'high ratio' because 1/6 is a larger (higher) number than say 1/8 which would be 10:80, meaning the kart would accelerate faster but have a lower top speed as might be called 'low ratio'. This is why some people talk about gearing 'up' to a speed, meaning put less teeth on the rear while others talk about gearing up to get acceleration meaning put more teeth on the rear.
Quite simply, it is a calculation that if you can gain a second over a rival down the straight by using less teeth but only lose half a second through the corners, then use less teeth, but if your rival can gain two seconds on you through the corners, then you might need to use more teeth.
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