Questions pupils ask: does a remote-controlled toy car violate Newton’s laws of motion?

<p dir="ltr">This might sound more like a physics question than a mathematics question, but I have found that some version of this question often comes up when teaching mechanics as part of A-level mathematics. I am often surprised how far students can get, successfully answering questions out of the textbook, and in examinations, with still a quite flaky understanding of Newton’s three laws of motion. The most prominent of Newton’s laws of motion for students is the second law because this is the one that can be encapsulated within a nice formula: “Force equals mass times acceleration” (Note 1). We are forever solving problems by saying things like, “Applying N2L to the car in the positive 𝑥 direction, …”, followed by writing down one or more equations, which we go on to solve to find a force, a mass or an acceleration. But what about the other two laws? I have heard students ask why we ‘never use them’, and I think that lack of understanding of those laws lies behind much student confusion.