Velocity and Acceleration Vector Decomposition on a Parametric Curve

This example demonstrates how to decompose the velocity and acceleration vectors into components parallel and perpendicular to the position vector along a parametric curve. Core mathematical concepts include parametric equations, derivatives, vector decomposition, and the geometric interpretation of velocity and acceleration. Construction highlights: using GeoGebra commands such as Derivative to compute first and second derivatives, CurveCartesian to define the parametric curve, If and Textfield for conditional display and input, and sliders (tmax, tmin) to adjust the parameter range. Key objects include f, g and their derivatives, the velocity vector v, acceleration vector a, position vector r, and constructed parallel components v_r, v_p and perpendicular components a_v, a_p, with ScaleVelocity and ScaleAcceleration to adjust vector lengths for clarity. Suitable for advanced high school or university courses in calculus and vector analysis, providing an intuitive understanding of tangential and normal acceleration decomposition in curvilinear motion.