Converting Speed Units: Kilometers per Hour to Meters per Second

This solution explains how to convert a speed given in kilometers per hour ($km/h$) to meters per second ($m/s$). We will take the specific value of $60 \text{ km/h}$ and demonstrate the conversion process step-by-step.

Calculating the Speed Conversion from km/h to m/s

To convert kilometers per hour ($km/h$) to meters per second ($m/s$), we need to understand the relationship between the units of distance (kilometers and meters) and the units of time (hours and seconds).

• Distance conversion: 1 kilometer is equal to 1000 meters ($1 \text{ km} = 1000 \text{ m}$).
• Time conversion: 1 hour is equal to 3600 seconds ($1 \text{ hour} = 60 \text{ minutes} \times 60 \text{ seconds/minute} = 3600 \text{ s}$).

We start with the given speed: $$ 60 \text{ km/h} $$ Now, we substitute the units with their equivalents in meters and seconds.

Replace 'km' with '1000 m': $$ 60 \frac{\text{km}}{\text{h}} = 60 \times 1000 \frac{\text{m}}{\text{h}} = 60000 \frac{\text{m}}{\text{h}} $$

Replace 'h' in the denominator with '3600 s': $$ 60000 \frac{\text{m}}{\text{h}} = \frac{60000 \text{ m}}{3600 \text{ s}} $$

Perform the division: $$ \frac{60000}{3600} \frac{\text{m}}{\text{s}} = \frac{600}{36} \frac{\text{m}}{\text{s}} $$ We can simplify this fraction further by dividing both the numerator and the denominator by common factors. Dividing both by 6 gives: $$ \frac{100}{6} \frac{\text{m}}{\text{s}} $$ Dividing by 2 gives: $$ \frac{50}{3} \frac{\text{m}}{\text{s}} $$

To get a more common representation, we convert the fraction to a decimal: $$ \frac{50}{3} \approx 16.67 $$ So, the speed is approximately $16.67 \text{ m/s}$.

Shortcut Method for Speed Conversion

A commonly used shortcut for converting $km/h$ to $m/s$ involves multiplying by the factor $\frac{5}{18}$. This factor is derived from the conversion steps above:

Using this shortcut for $60 \text{ km/h}$: $$ 60 \text{ km/h} \times \frac{5}{18} \frac{\text{m/s}}{\text{km/h}} $$ Calculate the result: $$ \frac{60 \times 5}{18} \frac{\text{m}}{\text{s}} = \frac{300}{18} \frac{\text{m}}{\text{s}} $$ Simplify the fraction by dividing the numerator and denominator by 6: $$ \frac{50}{3} \frac{\text{m}}{\text{s}} $$ As a decimal, this is approximately $16.67 \text{ m/s}$.

Conclusion

Therefore, the speed of $60 \text{ km/h}$ is equivalent to approximately $16.67 \text{ m/s}$. This conversion is crucial in physics and everyday applications where different units of speed are used.