Question

Convert \(2.155 \mathrm{~m} / \mathrm{s}\) into kilometers/hour.

Short answer

2.155 m/s is 7.758 km/h.

Step-by-step solution

Understand the Units

We start with a speed given in meters per second (m/s), and we want to convert it to kilometers per hour (km/h). Recall that 1 m = 0.001 km and 1 hour = 3600 seconds.

Convert Meters to Kilometers

We have 2.155 meters. To convert meters to kilometers, multiply by the conversion factor 0.001. \[ 2.155 ext{ m} imes 0.001 rac{ ext{km}}{ ext{m}} = 0.002155 ext{ km} \]

Convert Seconds to Hours

Since velocity is given per second and we want per hour, convert the time units from seconds to hours. Multiply the speed by 3600 (the number of seconds in one hour):\[ 2.155 ext{ m/s} imes 3600 ext{ s/h} = 7758 ext{ m/h} \]

Convert Meters per Hour to Kilometers per Hour

Now we have a speed of 7758 meters per hour. To convert this to kilometers per hour, we need to change meters to kilometers by dividing by 1000:\[ 7758 ext{ m/h} imes 0.001 rac{ ext{km}}{ ext{m}} = 7.758 ext{ km/h} \]

Final Result

The conversion from meters per second to kilometers per hour is complete: 2.155 m/s = 7.758 km/h.

Key concepts

Meters per second

Meters per second (m/s) is a unit of speed, which describes how many meters an object travels in one second. It is commonly used in scientific contexts, especially in physics, as it provides a straightforward way to express velocities in a metric system.
Understanding this unit is crucial when dealing with calculations involving speed and acceleration. Here are some key aspects you should know about meters per second:

• Basic Definition: It simply measures the distance in meters traveled every second.
• Applications: Used in various scientific studies and calculations, like the speed of a car over a specific course or the velocity of an object in free fall.
• Conversion Needs: While it is concise and widely used, meters per second might need to be converted to other units depending on the context, such as kilometers per hour in traffic analysis.

Kilometers per hour

Kilometers per hour (km/h) is another unit of speed often used in everyday situations, especially within the transportation sector. It tells you how many kilometers an object moves in one hour.
This unit is particularly helpful in contexts where distances and times are relatively large, such as travel speed in cars or public transport.

• Basic Definition: It represents how many kilometers are covered in an hour.
• Common Usage: Typically used on road signs and vehicle speedometers around the world.
• Converting with Simplicity: When measurements initially given in meters per second need to be understood in a more practical, day-to-day framework, converting to km/h is beneficial.

Conversion factors

Conversion factors are essential tools when transitioning one unit of measurement to another. They allow us to translate distances, weights, and other values into new forms without actual physical transformations.
In the exercise, the main conversion factors used were those converting meters to kilometers and seconds to hours.

• Meter to Kilometer: Since 1 meter is 0.001 kilometers, multiply by 0.001 to convert.
• Seconds to Hours: As 1 hour equals 3600 seconds, you multiply by 3600 to change seconds to hours.
• Role: They ensure accuracy and coherence in unit conversions, facilitating proper communication and understanding of values across different contexts.

Time conversion

Time conversion is a fundamental part of unit conversion, especially in exercises involving speed. It involves changing time measurements from one unit to another, like seconds to hours or minutes to days.
This concept is widely applicable and essential in ensuring coherence in speed and distance calculations.

• Understanding the 3600 Factor: Since there are 3600 seconds in an hour, multiplying a value in m/s by 3600 converts it to m/h.
• Significance in Everyday Calculations: Such conversions allow you to seamlessly express velocities in terms that are meaningful for everyday situations, like travel times in hours.
• Practicing Conversions: Regular practice with time conversions helps maintain accuracy and build confidence in handling more complex unit conversions.