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# Graphical Representation of Velocity and Acceleration

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Graphical Representation of Velocity and Acceleration

Ex) Construct a graph of position vs. time.
At time 0s, a runner is at position 0m At time 1.00s, the runner is at position 2.00m At time 2.00s, the runner is at position 4.00m

Slope = Dy/Dx Slope = Ds/Dt Slope = v

Rules for Position vs. Time Graph
The slope is equal to velocity If linear, v is constant (i.e. no acceleration) If linear and horizontal the object is stationary (i.e. the speed is zero) If linear, horizontal, and along the x-axis, the object is stationary at the origin. If the graph is not linear, the object’s velocity is changing. (i.e. the object is accelerating) The slope of the tangent line is equal to instantaneous velocity.

Ex) Construct a graph of velocity vs. time.
At time 0s, a car is at velocity 5.00m/s At time 3.00s, the car is at velocity 23.0m/s At time 6.00s, the car is at velocity 41.0m/s

Slope = Dy/Dx Slope = Dv/Dt Slope = a

Rules for Velocity vs. Time Graph
The slope is equal to acceleration. If linear, a is constant (i.e. constant acceleration) If linear and horizontal the object is not accelerating (i.e. the speed is constant) If linear, horizontal, and along the x-axis, the object is stationary. If the graph is not linear, the object’s acceleration is varying. The slope of the tangent line is equal to instantaneous acceleration.

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