Physics is learned from educators, books which describe physical reality and simple experiments. A scientific language is developed. Matter, space and time are beginning ideas.

Physics uses algebra and algebra uses geometry. As a "refresher" exercise
prove: (A - B)² = A² - 2AB + B².

The connected mechanical parts whereby explosive combustion becomes power of a rotating shaft are called "power trains." The simplest arrangement, crank-rod-piston, shown. Engine designers must know precisely the position and speed of the piston face for every position of the crank. The math tool, vectors, makes such tasks logically systematic.

When detail is unavailable, approximation is required.
"A dog runs back and forth between its two owners, who are walking toward one another... What distance will the dog have traveled when the three meet?"

Two boys, walking beside railroad tracks heard a train approaching from behind. The older boy knew the city train speeds limit was 30 mph. He and his buddy walked about 3 feet per second. When the nose of the engine was abreast of them, the smaller boy began to count. The count, the instant the caboose passed, was, "... 34 seconds." A moment later, the older boy said, "... only about 1400 feet long."

The idealization "ideal piston/cylinder apparatus" (is friction free and does not leak.) is useful.