AP Physics C: Mechanics / Unit 1: Kinematics
1.2 Displacement, Velocity, and Acceleration
Notes
- $\Delta x=x_f-x_i$; $\displaystyle v_{avg}=\frac{\Delta x}{\Delta t}$; $\displaystyle a_{avg}=\frac{\Delta v}{\Delta t}$.
- Constant acceleration: $v=v_0+at$, $\displaystyle x=x_0+v_0t+\frac{1}{2}at^2$, $v^2=v_0^2+2a\Delta x$.
Practice
A car speeds from 0 to 20 m/s in 4 s. Its acceleration:
$\displaystyle \frac{20}{4}$.
Starting from rest with $a=2$ m/s², the distance in 3 s:
$\displaystyle \frac{1}{2}(2)(9)$.
A ball is thrown straight up. At the top, its acceleration is:
Gravity still acts.
$x(t)=4t^3-2t$ (m). The velocity at $t=1$ s:
$\displaystyle v=\frac{dx}{dt}=12t^2-2$.
$a(t)=6t$ m/s² and $v(0)=2$ m/s. Then $v(2)=$
$\displaystyle v=2+\int_0^2 6t\,dt=2+12$.
Ready for more? Take the Unit 1 test.