AP Calc BC: Vectors

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9 Terms

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Position Vector
< x(t) , y(t) >
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Velocity Vector
< x’(t), y’(t)> for < dx/dt , dy/dt >
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Acceleration Vector
< x’’(t), y’’(t)>
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Speed (magnitude of velocity vector)
√\[x’(t)\]² + \[y’(t)\]²
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Displacement (linear distance between starting and ending positions)
√(x₂-x₁)² + (y₂-y₁)²
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Instantaneous Angle
arctan (dy/dx)
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Slope of Path
dy/dx = <dy/dt, dx/dt>
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Arc Length
∫a to b √(dx/dt)² + (dy/dt)² dt
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Area of a Region bounded by a polar graph
1/2 ∫ a to b r² dθ