AP Calc BC Parametric and Vector Motion Equations

memorize for your next quiz

Position

<x(t), y(t)>

Velocity

<V_x(t), V_y(t)> or <x’(t), y’(t)>

Acceleration

<V_x’(t), V_y’(t)> or <x’’(t), y’’(t)>

Displacement

\int_{a}^{b}\vec{v}(t)dt or \Delta x = \int_{a}^{b}V_x(t)dt; \Delta y = \int_{a}^{b}V_y(t)dt

Speed

|\vec{v}(t)| or \sqrt{(x’(t))^{2}+(y’(t))^{2}} or\sqrt{(V_x(t))^{2}+(V_y(t))^{2}}

Distance

\int_{a}^{b}\text{speed } dt; \int_{a}^{b}|\vec{v}(t)|dt or \int_{a}^{b}\sqrt{(V_x(t))^{2} + (V_y(t))^{2}} dt