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Physics 151 Week 4 Day 3 Topics – – – – Motion Diagrams Motion Graphs Area under a curve (velocity to position) Constant acceleration equations Motion Diagrams (a.k.a. Motion Maps) The motion diagrams below show an initial point 0 and a final point 1. A pictorial model would define five symbols, x0 and x1 (or y0 and y1), v0x and v1x, and ax. Determine whether each of these quantities is positive, negative, or zero. place either +, --, or 0 in each cell of the table below. These are motion diagrams with axes. For this problem, you have to figure out which positions, velocity components and acceleration components are negative (--), positive (+), or zero for one motion interval. – "0" on the axis indicates the origin and the "x" or "y" indicates the positive x or y direction respectvely. – The "0" on the motion diagram represents the initial position of the object for the motion interval shown. – The "1" on the motion diagram represents the final position of the object for the motion interval shown. A x0 x1 V0x v1x ax Slide 2-4 Motion Maps for + / - vx and ax Slide 2-4 Motion Graph Demonstrations Slide 2-4 Velocity Graph => Acceleration Graph vx slope of x vs. t graph ax slope of vx vs. t graph Slide 2-4 x = area under vx vs. t graph 1 1 x area b h t vx 2 2 Slide 2-4 vx = area under ax vs. t graph vx area b h t ax Slide 2-4 General Motion Model Graph Relationships vx slope of x vs. t graph ax slope of vx vs. t graph x area under vx vs. t graph vx area under ax vs. t graph Slide 2-4 Constant Acceleration Equations vx area b h t ax vx a x t v1x v0 x ax t (equation 1) x area under vx vs. t x Area1 (square) Area2 (triangle) 1 1 x bh1 bh2 t v0 x t v1x 2 2 1 x t v0 x t a t 2 1 x v0 x t ax t 2 (equation 2) 2 Area 2 Area 1 Slide 2-4