Dimensional Reasoning Math Example 3

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

easy

Convert 60 km/h to m/s using dimensional analysis.

1
Multiply by conversion factors: $60 \frac{\text{km}}{\text{h}} \times \frac{1000\text{ m}}{1\text{ km}} \times \frac{1\text{ h}}{3600\text{ s}}$ .
2
Cancel units: km cancels, h cancels. Result: $\frac{60 \times 1000}{3600}\frac{\text{m}}{\text{s}} = \frac{60000}{3600}\frac{\text{m}}{\text{s}} = \frac{50}{3}\text{ m/s} \approx 16.67\text{ m/s}$ .

Answer

60\text{ km/h} = \frac{50}{3}\text{ m/s} \approx 16.67\text{ m/s}

Dimensional analysis converts units systematically by multiplying by fractions equal to 1 (e.g.,

\frac{1000\text{ m}}{1\text{ km}} = 1

). Unwanted units cancel, leaving the desired units.

About Dimensional Reasoning

Using the units and dimensions of physical quantities to check formulas, guide derivations, and eliminate impossible answers.

Use dimensional analysis to find the units of pressure, given that pressure [formula], force is in N

A formula for the period of a pendulum is proposed as [formula] where [formula] is length (m) and [f

A student writes [formula] for Einstein's mass-energy formula. Use dimensional reasoning to explain