Graphs of Linear Motion. Graph of v vs. t vovo  t = 2  v = 4 Slope = acceleration.

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Presentation transcript:

Graphs of Linear Motion

Graph of v vs. t vovo  t = 2  v = 4 Slope = acceleration

Graph of d vs. t xoxo Tangent line Slope = instantaneous speed

Rule for Derivative

Derivative Relationships

Area under v vs. t Area = v o t Area = ½ (at) t= ½ at 2

Rule for Integral

Integral Relationships

Problem #1 The position of a particle is given by the equation x(t) = 4t 3 + 6t 2 + 7t What are: A)The function v(t) B)The function a(t) C)The instantaneous speed at 5 seconds D)The instantaneous acceleration at 3 seconds

Problem #2 The acceleration of a particle is given by the equation a(t) = 3t + 2. If the particle started from x 0 = 3 m and v o = 0, What are: A)The function v(t) B)The function x(t) C)The instantaneous speed at 5 seconds D)The position of the particle at 4 seconds

Problem #3 What is the distance covered from 0 to 10 seconds? What is the acceleration at 7 seconds?

What is the distance covered from 0 to 6 seconds? What is the displacement at 6 seconds if x o =0? Problem #4