position time position time tangent! derivatives are the slope of a function at a point slope of x...
TRANSCRIPT
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Calculus in 10 Minutes or Less
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Slope
position
time
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Slope
position
time
tangent!
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Derivatives
Derivatives are the slope of a function at a point Slope of x vs. t
velocity - describes how position changes over time Slope of v vs. t
acceleration - describes how velocity changes over time
Slope of a vs. t jerk - describes how acceleration changes over time
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Derivatives
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Derivative Rules
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If the position of an object is described by the function
What are the velocity and acceleration functions?
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Area
velocity
time
Easy!
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Area
velocity
time
Harder!!!
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Integrals
Integrals are anti-derivatives Graphically, integrals are the area
under a curve Area under a v vs. t graph = Displacement
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Integrals
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Integral Rules
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An object’s acceleration is described by a(t) = 2t. Find the velocity and position functions.
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Initial ConditionsIf x = 5 when t = 0, what is the displacement function for this velocity function?
-so- -so-
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Definite Integrals
Taking the integral from one point to another.
Same rules apply, but don’t have to do “+C”
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Find the displacement from t = 2 seconds to t = 4 seconds for the velocity function
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