AP Calculus AB / Unit 4: Contextual Applications of Differentiation
4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
Notes
- Velocity $v(t)=x'(t)$; acceleration $a(t)=v'(t)=x''(t)$.
- Speed is $|v(t)|$.
- The particle moves right when $v>0$, left when $v<0$, and changes direction where $v$ changes sign.
- Speeding up when $v$ and $a$ have the same sign; slowing down when they differ.
Practice
$v(3)=-2$ and $a(3)=4$. At $t=3$ the particle is:
Opposite signs mean slowing down.
$x(t)=t^2-4t$. When does the particle change direction?
$v=2t-4$ changes sign at $t=2$.
A particle's velocity is $-5$. Its speed is:
Speed is the absolute value of velocity.
Ready for more? Take the Unit 4 test.