Question

The 2014 Tesla Roadster, an all-electric car, has a top speed of 125 miles per hour. Calculate the speed in centimeters per second.

Short answer

5532.43 centimeters per second

Step-by-step solution

Convert miles to kilometers

First, convert the speed from miles per hour to kilometers per hour. Use the conversion factor that 1 mile is approximately equal to 1.60934 kilometers. Calculate the speed in kilometers per hour as follows:\[ 125 \text{ miles per hour} \times 1.60934 \text{ kilometers per mile} = 201.1675 \text{ kilometers per hour} \]

Convert kilometers to meters

Next, convert the speed from kilometers per hour to meters per hour. Since 1 kilometer equals 1000 meters, multiply the speed in kilometers per hour by 1000:\[ 201.1675 \text{ kilometers per hour} \times 1000 \text{ meters per kilometer} = 201167.5 \text{ meters per hour} \]

Convert hours to seconds

Now, convert the speed from meters per hour to meters per second. There are 3600 seconds in one hour, so divide the speed in meters per hour by 3600:\[ 201167.5 \text{ meters per hour} \times \frac{1}{3600} \text{ hours per second} = 55.3243 \text{ meters per second} \]

Convert meters to centimeters

Finally, convert the speed from meters per second to centimeters per second. Since 1 meter equals 100 centimeters, multiply the speed in meters per second by 100:\[ 55.3243 \text{ meters per second} \times 100 \text{ centimeters per meter} = 5532.43 \text{ centimeters per second} \]

Key concepts

Speed Conversion

Understanding how to convert speed is crucial for solving various problems in physics and everyday life. Speed conversion involves changing a speed value from one unit to another. In the given problem, we needed to convert the top speed of the Tesla Roadster from miles per hour to centimeters per second.

To do this, we followed a step-by-step process that involved multiple conversions. Initially, we converted from miles to kilometers. Then, we converted kilometers to meters, meters per hour to meters per second, and finally meters to centimeters. Each step uses specific conversion factors, making it critical to understand and remember corresponding relationships between units of measurement.

Metric System

The metric system is a standardized system of measurements used globally, making it easier to share and understand measurements across different regions and scientific disciplines. This system is based on units like meters for length, kilograms for mass, and seconds for time, with prefixes like 'centi' and 'kilo' indicating fractions or multiples of these base units.

In the given exercise, we used metric units such as kilometers, meters, and centimeters to convert the speed. Knowing that 1 kilometer equals 1000 meters and 1 meter equals 100 centimeters streamlined the process.

Distance and Time Calculations

To convert speed from one unit to another, a clear understanding of the relationship between distance and time is needed. Speed is defined as distance traveled per unit of time, and it's measured in units like miles per hour or meters per second.

In this exercise, converting from miles per hour to centimeters per second involved multiple calculations:

• First, converting distance units (miles to kilometers to meters to centimeters)
• Then, converting time units (hours to seconds)

Making these conversions allowed us to calculate the speed accurately in the desired unit.

Dimensional Analysis

Dimensional analysis is a method used to convert one unit to another using conversion factors. It ensures that the final units make sense and the calculations are valid. This technique involves multiplying by fractions equal to one, where the numerator and denominator represent the same quantity but in different units.

Let's recap the exercise:

• We started with 125 miles per hour and converted miles to kilometers using the factor 1.60934 km per mile.
• Next, we converted kilometers to meters relying on 1 km = 1000 meters.
• Then, we adjusted the time unit from hours to seconds, noting that 1 hour = 3600 seconds.
• Finally, we converted meters to centimeters by recognizing that 1 meter = 100 centimeters.

Each conversion used precise equivalences, transforming miles per hour into centimeters per second seamlessly.