Question

The 2013 Rolls Royce Ghost Alpine has a top speed of 155 miles per hour. Calculate the speed in centimeters per second.

Short answer

6,929.12 cm/s

Step-by-step solution

- Convert Miles per Hour to Centimeters per Hour

First, recognize that 1 mile = 160,934.4 centimeters. Therefore, to convert from miles per hour to centimeters per hour, multiply the speed in miles per hour by 160,934.4: \( 155 \text{ miles per hour} \times 160,934.4 \text{ cm/mile} = 24,944,832 \text{ cm/hour} \)

- Convert Hours to Seconds

Next, convert hours to seconds by noting that 1 hour = 3,600 seconds. We need to divide the result from Step 1 by 3,600 to convert the speed to centimeters per second: \( \frac{24,944,832 \text{ cm/hour}}{3,600 \text{ s/hour}} = 6,929.12 \text{ cm/s} \)

Key concepts

Speed Conversion

Understanding speed conversion is crucial in chemistry and many other fields. Speed is often expressed in different units depending on the context and region. To solve problems involving speed, you need to know how to convert between these units accurately. Converting between units makes it easier to compare and analyze data.

Speed is typically given in terms of distance per unit time, like miles per hour (mph) or centimeters per second (cm/s). Converting between these units involves multiplying or dividing by factors that convert the distance and time components separately. Let's delve into this with the example involving the Rolls Royce Ghost Alpine's top speed.

Centimeters per Second

Centimeters per second (cm/s) is a speed unit that expresses how many centimeters an object travels each second. It's a metric unit commonly used in scientific contexts where precise measurements are crucial. Understanding cm/s requires knowing the basic relationships between various distance and time units.

For example, 1 meter equals 100 centimeters, and 1 hour equals 3,600 seconds. By understanding these relationships, you can easily convert between larger and smaller units. The key step is performing the calculations correctly, ensuring that you apply the conversion factors correctly.

In the problem given, we first convert miles per hour to centimeters per hour. This is done using the conversion factor: 1 mile = 160,934.4 centimeters. Multiplying 155 miles by 160,934.4 centimeters per mile gives the result of 24,944,832 centimeters per hour.

Miles per Hour to cm/s

Miles per hour (mph) is a common speed unit in countries using the Imperial system. To convert mph to cm/s, you need to convert both the distance (miles to centimeters) and the time (hours to seconds). This is a two-step process.

First, convert miles to centimeters. For this, remember that 1 mile equals 160,934.4 centimeters. Multiply the speed in miles per hour by 160,934.4 to get the speed in centimeters per hour. For the Rolls Royce Ghost Alpine with a top speed of 155 mph, this results in:

\[155 \text{ mph} \times 160,934.4 \text{ cm/mile} = 24,944,832 \text{ cm/hour}\]

Next, convert hours to seconds. Since 1 hour equals 3,600 seconds, you divide the speed in centimeters per hour by 3,600 to get the speed in centimeters per second:

\[\frac{24,944,832 \text{ cm/hour}}{3,600 \text{ s/hour}} = 6,929.12 \text{ cm/s}\]

Thus, the top speed of the Rolls Royce Ghost Alpine in centimeters per second is 6,929.12 cm/s. By following these steps, you can easily convert any speed given in miles per hour to centimeters per second.