Lens sharpness is fairly complex topic as there are many variables that dictate what makes an image sharp and what does not.
Here I will try and keep it as basic as possible with a just a few areas that can be considered regarding sharpness.

It is generally true that Prime Lenses  are sharper than Zoom Lenses.
The reason for this is due to a prime Lens not having the extra lens elements to correct for diffraction as do zoom Lenses.

As a result, and this applies to even the cheapest of the Prime lenses, they are the masters of just one focal length with just one job to do, and generally, they do this fine, even the cheaper lenses.

Whereas, a zoom lens, has to get the sharpness correct over a much larger focal range. The bigger the range, the tougher the job and more scope for errors, but that is not to say that they are not able to correct for any errors and still produce a relatively sharp image.

A $100 50mm f/1.8 may result in very sharp, edge to edge images at say f/8, but a $300 70-200mm f4.0 may actually end up being sharper edge to edge at 80mm and f/16, better known as the lens' sweet spot.

On the other hand, a $2000 Zoom Lens may end up being way sharper throughout the entire focal range of 70-200mm, it can all be relative.

In Zoom lenses, to keep the overall lens size down and to keep focal issues at bay, correction has to be made by introducing a further lens element just behind the main lens to reduce the distance to the sensor. This second lens has to be positioned just right so that it does not produce any chromatic aberration. Several of these elements are positioned within these lenses and each group is there for the correction of CA, reflections, contrast and sharpness.

Therefore, we have to take note that each group is also creating its own set of challenges, and the subsequent groups, along with keeping the size down, are also trying to correct the previous groups reflections and errors.

However, we also have to assume that the more expensive zoom lenses, will have better quality glass, with higher quality elements and grouped more efficiently than say a budget Zoom, and therefore, yield a sharper edge to edge image.

As further research, you maybe interested in reading about MTF, Modulation Transfer Function and how this measure is used in determining sharpness of a lens

Are prime lenses sharp across the whole frame while zoom lenses are soft in the corners?
I have a road bike with a front brake that wears a lot of brake pad when I ride downhill every day. I lose 900ft in elevation on steep grades with lots of stop signs and traffic lights. On top of that, it rains a decent amount and the rim brakes are terrible in that weather. I don't trust them downhill in the rain. Sometimes I just walk.

I feather the brakes going downhill, because otherwise I'm too fast to stop quickly for an errant car.

It'd be nice to not constantly replace pads, and have powerful stopping. How can I make this constant downhill more pleasant?

Thanks. 
