Physics / Unit 1: Motion in One Dimension
1.4 Motion Graphs
Notes
Graphs show motion at a glance. Read the slope and the area.
| Graph | Slope means | Area under curve means |
|---|---|---|
| position vs time | velocity | (not used) |
| velocity vs time | acceleration | displacement |
- On a position-time graph, a flat line means the object is at rest; a straight sloped line means constant velocity; a curve means changing velocity.
- On a velocity-time graph, a flat line means constant velocity (zero acceleration).
- Example: a velocity-time graph is flat at $4 \text{ m/s}$ for 6 s. Displacement = area $= 4 \times 6 = 24 \text{ m}$.
Practice
On a position-time graph, an object's line is horizontal. What is the object doing?
The position does not change, so the velocity (slope) is zero.
A velocity-time graph is a straight line from $0 \text{ m/s}$ at $t = 0$ to $12 \text{ m/s}$ at $t = 4 \text{ s}$. What is the acceleration?
Slope $\displaystyle = \frac{12 - 0}{4 - 0} = 3 \text{ m/s}^2$.
A velocity-time graph rises in a straight line from 0 to 12 m/s over 4 s, what is the displacement?
Area of the triangle $\displaystyle = \frac{1}{2}(4)(12) = 24 \text{ m}$.
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