The cross diagram is a way to illustrate and plan the solutions for all kinds of constant-acceleration kinematics problems—including projectile motion, multistage, and multiple-object problems. The cross diagram arranges the kinematic variables in a logical way, making the kinematic relationships between them easy to identify. Combined with a method to visually mark known information and equations, it provides a framework to plan out which equations will be used in the solution of a problem. This paper introduces the cross diagram through its use in a series of example problems.
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Three of the equations (a, b, and e from Fig. 1) can be graphically derived for students from three different ways of computing the area of a trapezoid on a v–t diagram: a rectangle plus a triangle, a rectangle minus a triangle, and the average of the parallel sides times the width.
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An expanded description with simpler equations includes eight variables (x0, x1, v0, v1, ϕ0, ϕ1, A, and ω) with eight equations, four of them independent.
© 2022 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2022
Author(s)
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