In mathematics education, a vast amount of research has shown that students of different ages have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. For example, in geometry it is known that many students believe that if the sides of a figure are doubled, the area is doubled too. However, also history of science provides several cases of thinkers who inadequately postulated linear relations to describe situations. This article focuses on secondary school students' over-reliance on linearity in physics. Now and then, science educators report students' tendency to assume and impose linear relations in physics, but--as far as we know--no substantial efforts were undertaken to study this phenomenon systematically. We conducted an empirical investigation aimed at identifying the competence of 8th- and 11th-graders--before and after being taught the relevant physical topics--to qualitatively grasp various situations in physics, as well as their tendency to quantify that qualitative insight linearly. The results provide an ambivalent picture of students' overuse of linearity in physics: Although linear reasoning is sometimes used as a default strategy, even after instruction that addresses the relevant physical contents, this study also indicates that context is taken into account more often than is suggested by research on mathematical problem solving.