Perform the following conversions: (d) 0.510 in./ms to km/hr

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Step 1: Identify the conversion factors. We know that 1 inch equals 2.54 centimeters, 1 meter equals 100 centimeters, 1 kilometer equals 1000 meters, 1 second equals 0.001 milliseconds, and 1 hour equals 3600 seconds.

Step 2: Start with the given value, 0.510 in./ms. We want to convert inches to kilometers and milliseconds to hours.

Step 3: Convert inches to kilometers. First, convert inches to centimeters using the conversion factor 1 inch = 2.54 cm. Then, convert centimeters to meters using the conversion factor 1 m = 100 cm. Finally, convert meters to kilometers using the conversion factor 1 km = 1000 m.

Step 4: Convert milliseconds to hours. Use the conversion factor 1 second = 0.001 milliseconds to convert milliseconds to seconds. Then, convert seconds to hours using the conversion factor 1 hour = 3600 seconds.

Step 5: Multiply the original value by the conversion factors. The units of inches and milliseconds should cancel out, leaving you with the final units of kilometers per hour.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. This involves using conversion factors, which are ratios that express how many of one unit are equivalent to another. For example, to convert inches to kilometers, one must know the relationship between these units, such as 1 inch equals 0.0000254 kilometers.

Speed and Velocity

Speed is a scalar quantity that represents the rate of motion, defined as the distance traveled per unit of time. It is typically expressed in units such as meters per second (m/s) or kilometers per hour (km/hr). Understanding speed is crucial for conversions, as it allows for the comparison of different units of measurement in terms of how fast an object is moving.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one set of units to another by analyzing the dimensions involved. It involves multiplying by conversion factors that cancel out the original units, leaving the desired units. This method ensures that the calculations are consistent and accurate, making it a powerful tool in solving problems involving unit conversions.