Chapter 1, Problem 59QP

Interpretation Introduction

Interpretation:

The speed of the jogger running the given distance is to be calculated in in/s, m/min, and km/h.

Concept introduction:

Dimensional analysis is a way to convert the units of measurement. In order to convert one unit to another, one needs to know the relationship between those units. These relationships are called conversion factors. Dimensional analysis is used to set up and solve a unit conversion problem using conversion factors.

Conversion factor is a fraction obtained from a relationship between the units. It is written as a ratio, and can be inverted to give two conversion factors for every relationship.

$\text{1 mile}=\text{1609 m}$, to convert miles to meter, the conversion factor is $\frac{\text{1609 m}}{\text{1 mile}}$.

$\text{1 m = 100 cm}$, to convert m to centimeter, the conversion factor is $\frac{\text{100 cm}}{\text{1 m}}$.

$\text{1 in = 2}\text{.54 cm}$, to convert centimeter to inch, the conversion factor is $\frac{\text{1 in}}{\text{2}\text{.54 cm}}$.

$1\text{ min}=60\text{ s}$, to convert minute to second, the conversion factor is $\frac{60\text{s}}{1\min }$.

$1\text{hr = 60 min}$, to convert minute to hour, the conversion factor is $\frac{1\text{hr}}{60\min }$.