2026-02-08 21:38

Status: #developing

Tags: #physic

Uniformity and Acceleration

Uniform Motion

• Motion at a constant velocity
• Covers a consistent displacement regardless of time period (give domain is restricted)

Non-Uniform Motion

• Velocity changes in the $\overrightarrow{v}(t)$ function given there is a restricted domain
• Changes speed of object in a direction

Acceleration ($\overrightarrow{a}$)

• Rate of change in velocity given there is a restricted domain
  • $\overrightarrow{a}=\frac{\mathrm{\Delta }\overrightarrow{v}}{\mathrm{\Delta }\overrightarrow{t}}$
• Uniform Accelerated Motion defines $\overrightarrow{a}$ as a constant

Graph Relationships

• Derivative of $\overrightarrow{r}vst$ graph describes the $\overrightarrow{v}vst$ graph
• Derivative of $\overrightarrow{v}vst$ graph describes the $\overrightarrow{a}vst$ graph
• Area of $\overrightarrow{v}vst$ graph describes $\mathrm{\Delta }\overrightarrow{r}$ given t is in a restricted domain
  • $$A(t)={\int }_0^t\overrightarrow{r}(t)dt$$
• Area of $\overrightarrow{a}vst$ graph describes $\mathrm{\Delta }\overrightarrow{v}$ given t is in a restricted domain
  • $$A(t)={\int }_0^t\overrightarrow{v}(t)dt$$

References

1.2 Speed and Velocity