| Quantity | SI Unit | Dimensional Formula |
|---|---|---|
| Displacement | m | [L] |
| Velocity | m/s | [LT^{-1}] |
| Acceleration | m/s^2 | [LT^{-2}] |
| Time | s | [T] |
| Jerk | m/s^3 | [LT^{-3}] |
Verification technique: Every term in an equation must have the same dimensions.
Example: Check s = ut + (1/2)at^2
- [s] = [L]
- [ut] = [LT^{-1}][T] = [L] ✓
- [at^2] = [LT^{-2}][T^2] = [L] ✓
Deriving unknown relations: If T (time of flight) depends on u, g, theta: T = k * u^a * g^b * (theta is dimensionless) [T] = [LT^{-1}]^a * [LT^{-2}]^b => L: 0 = a + b => b = -a => T: 1 = -a - 2b = -a + 2a = a => a = 1, b = -1 => T = k * u/g (which matches T = 2sin(theta) * u/g)