Applications of Differentiation
Context
Differentiation can be applied in various ways, one of which is physics.
| Scalars | Vectors | |
|---|---|---|
| Distance | Displacement | |
| Definition | A measurement of how far an object is from a fixed point of reference. Only magnitude (size) is measured. | Distance + Direction (e.g. cardinal directions like North, South, East, West, or Left/Right) |
| Example | 5 km away | 5 km North |
| Speed | Velocity | |
| Definition | A rate of change (derivative, gradient) of distance over time. Only magnitude (size) is measured. | Speed + Direction |
| Example | 15 km/h | 15 km/h to the positive direction |
Notations
If x is a function of time,
Thus,
v is for velocity, a is for acceleration.