Dimensional Consistency Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Is the equation v=d+tv = d + t (velocity = distance + time) dimensionally consistent?

Solution

  1. 1
    Step 1: [v]=m/s[v] = \text{m/s}, [d]=m[d] = \text{m}, [t]=s[t] = \text{s}.
  2. 2
    Step 2: m+s\text{m} + \text{s} — you can't add meters and seconds!
  3. 3
    Step 3: Not dimensionally consistent. The equation must be wrong.

Answer

No, dimensionally inconsistent.
Dimensional consistency requires all terms being added or set equal to have the same units. You can only add quantities of the same dimension — this is a fundamental check for equation validity.

About Dimensional Consistency

The principle that every term added or equated in a valid equation must share the same physical dimensions or units.

Learn more about Dimensional Consistency →

More Dimensional Consistency Examples

Example 2 medium

Check: [formula] where [formula] is energy (kg·m²/s²), [formula] is mass (kg), [formula] is speed (m

Example 3 easy

Is [formula] a valid formula for area?

Example 4 medium

In the equation [formula] (where [formula] is in meters), are all terms dimensionally consistent?

← All Dimensional Consistency Examples Dimensional Consistency Concept