AP Calculus BC / Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions
Notes
- Speed: $\displaystyle |\vec v|=\sqrt{x'(t)^2+y'(t)^2}$.
- Distance traveled: $\displaystyle \int_a^b|\vec v(t)|\,dt$.
- Position: start position plus the integral of each velocity component.
Practice
$\vec v(t)=\langle 3,4\rangle$. Speed:
$\displaystyle \sqrt{9+16}$.
$\vec v(t)=\langle t,\,1\rangle$. Speed at $t=2$:
$\displaystyle \sqrt{4+1}$.
A particle moves left when:
Horizontal direction comes from $x'$.
Ready for more? Take the Unit 9 test.