I rarely see civilians taking carts in the city, but this is actually a very popular option in more rural parts of the country.
A faster (and more expensive) option for getting around is calling a cab. Most cabs within the city will cost less than 3000 CFA ($5). Calling a cab can be tricky, because you have to negotiate a price with the driver, and you cannot simply give the driver an address (as you would in the United States). You have to give the driver a notable landmark near where you are going, because, as I said before, addresses and streets are not as established here as they are in the United States.
These are all local options, but there are also public transportation options for getting to other parts of the country.
Taking the car rapide for the first time was actually a bit overwhelming, because I speak limited Wolof. I was a little intimidated asking the driver where it was going in my broken sentences, but he was very kind and understanding! Now I find the car rapide quite relaxing, and it makes me feel more integrated in my community because I am going to and from the research center with locals. Because I have a regular schedule, I can sometimes see familiar faces, which is always a good feeling.
You'll often see car rapides and ta-tas decorated with images of famous Muslim figures or religious sayings. The most popular is Cheikh Amadou Bamba, founder of the Mouride Islamic Brotherhood, the most common Muslim brotherhood in Senegal.