I'm not sure if this will work well for your purposes, but the same detection method for RPMs that you seem to want is used on bicycles. They usually mount a permanent magnet to a spoke of the wheel (in this case, you'd fix it onto the wheel hub with epoxy or something else nice and secure) and have a solenoid or similar in line with it. The magnet will generate a current in the solenoid or similar sensor when passing by, and you simply measure the time in seconds between two passes. However, I would caution you on sticking with this type of velocity measure, for reasons I'll detail below.
Doing this math is easy for a micro controller. That is 1R over n seconds, for RPS. Say you want meters per second or m/S; take your wheel diameter d and get the circumference with pi*d or 3.14159*d for a good approximation. That is obviously the distance covered, using whatever unit you chose to measure d with, per 1 rotation. So, (pi*d) * RPS = distance/second, or meters per second if you used meters for the diameter. This may seem obvious to you but it helps clarify my following points.
If you are going to be navigating a map, however, since you are using a fast moving, quickly accelerating and decelerating RC car as your robot, you may want to know distance travelled more than the current speed. Any measurement system that gets you your speed or velocity in the manor described above will not be great for this task. Any measurement system that detects the wheel once per rotation will have a distance resolution of only the circumference of your wheels. I'm not sure if you intended to do this, but if you did, I'd have to say it's an awful idea with that car body. Your wheels look to be around 5-66cm in diameter, meaning a circumference in the ballpark of 15-18 cm. That's already 1/6th to 1/5th of a meter of travel per rotation.
The fact that you have those tires on the car might also mess with distance and even velocity measurements if you are on uneven terrain or change directions quickly. Relying on rotations to judge distance and velocity is only accurate while your tires maintain the same radius, and soft foam- or air-filled tires will certainly deform from different weights or vertical movements, and if your wheel that has the sensor attached comes off a bump and spins freely for a second you've just wrecked your data. Basically, if you need wheels like those for the terrain you're on, and velocity detection method based on the wheel itself is useless. If you are dead set on this method and are on flat, even terrain, then switch to a harder wheel with good contact on flat surfaces. Otherwise, I'd strongly recommend an accelerometer for velocity data mounted on the body of the vehicle.
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I don't mean to be insulting and I'm sorry if any of this sounded accusatory, but I wouldn't want you making an easy mistake which would be avoided with an even simpler solution.
If you have any further questions, feel free to message me. I happen to be working on a project on a similar platform myself, so maybe we can compare notes
