Position vs. Time (PT) graphs Velocity vs. Time (VT) graphs

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Presentation transcript:

Position vs. Time (PT) graphs Velocity vs. Time (VT) graphs Motion Graphs 1 - Slope Position vs. Time (PT) graphs Velocity vs. Time (VT) graphs

Motion Graphs Pictorial representations of data (or predictions/calculations) There are two motion graphs that are normally analyzed Position vs. Time (PT) graphs d = Vit +(1/2)at2 (accelerated motion) d = Vt (constant motion, a = 0 so V = Vi = Vf) Velocity vs. Time (VT) graphs Vf = Vi + at (accelerated motion) Vf = Vi (constant motion, a = 0 trivial case)

Role of Slope A slope shows ratio of a change (m =DY/DX) A slope represents the rate that the Y changes with respect to how the X changes. For many motion graphs the X axis represents time Position vs. Time graph (in PT slope = velocity) Velocity vs. Time graph (in VT slope = acceleration) There are often 4 cases that have to be recognized Increasing slope Decreasing slope Constant slope No slope or slope is zero

Recognizing increasing slopes (Curving-up parabola) (Curving-down parabola) Graphs of slopes 2 4 6 1 3 5 2 4 6 1 3 5

Recognizing decreasing slopes (Curving-down parabola) (curving-up parabola) Graphs of slopes 2 4 6 1 3 5 2 4 6 1 3 5

Recognizing constant slopes Graphs of slopes 2 4 6 1 3 5 2 4 6 1 3 5

Recognizing No Slope (slope=0) Graphs of slopes 2 4 6 1 3 5 2 4 6 1 3 5

Slopes in PT and VT graphs Velocity is the slope of a Position vs. Time graph Acceleration is the slope of a Velocity vs. Time graph

Curving up or down (in PT graphs) Curving up or down describes the way the graph curves; in other words, how the slope is changing For a Position vs. Time graph the curving up or down represents the acceleration

Curving up or down (in PT graphs) Curving up parabola The object’s acceleration is + Curving down parabola The object’s acceleration is - No Curving The object’s acceleration is 0

Graphs of increasing velocity Position Acceleration + parabola - parabola Velocity + slope - slope Position

Graphs of decreasing velocity Position Acceleration - parabola + parabola Velocity + slope - slope Position

Sample Problem 1 From the Position versus Time graph shown, graph the velocity versus time graph. d (m) t (s) V(m/s) t (s)

Sample Problem 2 From the Position vs. Time graph shown, graph the Velocity vs. Time graph. For one moment here the slope is 0. d (m) t (s) V(m/s) t (s)