Three matchbox cars are traveling at different speeds and directions: 10 m/s northeast, 10 m/s southeast, and 15 m/s northeast. The document discusses using matchbox cars and their speeds and directions as an example to introduce concepts related to vectors, vector spaces, and tensors. It describes how the speeds of the cars can be added and multiplied together, forming a basis set and elements within a vector space to represent and operate on the cars and their motion.