Velocity & Acceleration Vectors

AP Calculus · Axiom Academy

LESSON Velocity & Acceleration Vectors Understanding motion through calculus Step 1: Velocity is the First Derivative When a position is described by a vector-valued function , the velocity is the rate of change of position: The velocity vector points in the direction of motion Step 2: Speed is the Magnitude of Velocity The speed is how fast you're moving (a scalar), which is the magnitude of the velocity vector: This is the familiar distance formula applied to the velocity vector! Step 3: Acceleration is the Second Derivative Acceleration measures how the velocity is changing: This is the second derivative of the position function. It tells us how the direction and magnitude of velocity are changing! Step 4: Tangent & Normal Components The acceleration vector can be decomposed into two parts: Speeds you up or slows you down along the curve Turns you toward or away from the curve's center

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