20 lines
962 B
Markdown
20 lines
962 B
Markdown
Motion in a straight line is one dimensional.
|
|
|
|
Kinematics or the physics of motion has 4 noteworthy parameters: time ($t$), position ($x$), velocity ($v$), and acceleration ($a$).
|
|
|
|
Kinematic problems have a start and end of motion.
|
|
|
|
# Displacement
|
|
|
|
Displacement is calculated with the formula:
|
|
$$\Delta x = \text{x-value of final position} - \text{x-value of initial posiion}$$
|
|
|
|
# Velocity
|
|
Average velocity over a time interval $\Delta t$ is defined to be: **the displacement** (net change in position), **divided by** **the time taken**.
|
|
|
|
$$ \bar{v} = \dfrac{\text{final position-initial position}}{\text{final time - initial time}} = \dfrac{x_2 - x_1}{t_2 - t_1} = \dfrac{\Delta x}{\Delta t}$$
|
|
**Speed (m/s)** is defined to be the total distance traveled divided by the time taken. Speed and velocity are *not the same*.
|
|
|
|
|
|
$$ v_{\text{instant}} = v = \lim_{\Delta t \to 0}\frac{\Delta x}{\Delta t} = \frac{dx}{dt}$$
|
|
- $x(t)$ -> position as a function of time |