position time position time tangent!  Derivatives are the slope of a function at a point  Slope of x vs. t  velocity - describes how position changes.

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Presentation transcript:

position time

position time tangent!

 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

If the position of an object is described by the function What are the velocity and acceleration functions?

velocity time Easy!

velocity time Harder!!!

 Integrals are anti-derivatives  Graphically, integrals are the area under a curve  Area under a v vs. t graph = Displacement

An object’s acceleration is described by a(t) = 2t. Find the velocity and position functions.

If x = 5 when t = 0, what is the displacement function for this velocity function? -so-

 Taking the integral from one point to another.  Same rules apply, but don’t have to do “+C”

Find the displacement from t = 2 seconds to t = 4 seconds for the velocity function