I have a 2002 Volvo S60. Can the speed sensors on this car cause it not to go over 15 mph?

Yes, absolutely. If your car is doing this, it is almost certainly in what is called "safe mode." From what I understand, Volvo cars go into "safe mode" automatically when the on-board computer senses that something might be wrong in the engine; therefore, the computer cuts power, i.e., prevents too much fuel from reaching the engine (which in turn keeps it under 10 or 15 mph). Usually, there will be a message on your display to signal safe mode (e.g., "Reduced Engine Performance"). In most cases, the computer will, as the mechanics say, be throwing various codes regarding the engine's performance. I am neither a Volvo mechanic nor a Volvo expert, though I do own a Volvo s60 (2004) close in years to yours. Mine has gone into safe mode a few times in the past year or so. Unfortunately in my case, it has been for a rather serious problem. However, I've been told that Volvos can go into safe mode for rather minor problems with relatively easy fixes. While some online sources can be helpful (e.g., here and Volvo forums), I would urge that you take the car to a mechanic who can hook it up to a computer, read the Volvo codes, and tell you what is wrong with it (i.e., causing safe mode). They shouldn't charge you much, if anything at all, to do this.