Question

Perform the following conversions. a) \(45.0 \mathrm{~m} / \mathrm{min}\) to meters/second b) \(0.000444 \mathrm{~m} / \mathrm{s}\) to micrometers/second c) \(60.0 \mathrm{~km} / \mathrm{h}\) to kilometers/second

Short answer

a) 0.75 m/s, b) 444 µm/s, c) 0.0167 km/s

Step-by-step solution

Convert Meters per Minute to Meters per Second

To convert from meters per minute to meters per second, divide the speed by 60 because there are 60 seconds in a minute. Given: \[ 45.0 \, \text{m/min} \]Conversion: \[ \frac{45.0 \, \text{m/min}}{60 \, \text{s/min}} = 0.75 \, \text{m/s} \]

Convert Meters per Second to Micrometers per Second

Converting meters to micrometers involves multiplying by 1,000,000 because there are 1,000,000 micrometers in a meter.Given:\[ 0.000444 \, \text{m/s} \]Conversion:\[ 0.000444 \, \text{m/s} \times 1,000,000 \, \text{µm/m} = 444 \, \text{µm/s} \]

Convert Kilometers per Hour to Kilometers per Second

To convert from kilometers per hour to kilometers per second, divide the speed by 3,600 because there are 3,600 seconds in an hour.Given:\[ 60.0 \, \text{km/h} \]Conversion:\[ \frac{60.0 \, \text{km/h}}{3,600 \, \text{s/h}} = 0.0167 \, \text{km/s} \]

Key concepts

Conversion from Meters per Minute to Meters per Second

When you want to convert a speed given in meters per minute (m/min) to meters per second (m/s), the key is understanding the relationship between minutes and seconds. First, remember that there are 60 seconds in one minute. So, to find out how many meters you travel in one second, you simply divide the number of meters you travel in a minute by 60. This is because dividing helps you break down how much is happening in a smaller time frame.For example, if you are traveling at \(45.0 \, \text{m/min}\), the conversion to meters per second would be:\[\frac{45.0 \, \text{m/min}}{60 \, \text{s/min}} = 0.75 \, \text{m/s}\]**Steps to remember:**

• Identify the speed in meters per minute.
• Divide by 60 to convert to meters per second.
• The result represents your speed per second.

Conversion from Meters per Second to Micrometers per Second

Converting meters per second (m/s) to micrometers per second (µm/s) involves understanding the metric conversion between meters and micrometers. One meter is equivalent to one million micrometers. This means if something is moving at a speed of 1 meter per second, it is the same as moving 1,000,000 micrometers per second.To convert a given speed in m/s to µm/s, you multiply the number of meters per second by 1,000,000.For instance, let's say you have a speed of \(0.000444 \, \text{m/s}\):\[0.000444 \, \text{m/s} \times 1,000,000 \, \text{µm/m} = 444 \, \text{µm/s}\]**Quick Tips:**

• Remember there are 1,000,000 micrometers in a meter.
• Multiply the given speed in m/s by 1,000,000.
• The result shows your speed in micrometers per second.

Conversion from Kilometers per Hour to Kilometers per Second

To convert from kilometers per hour (km/h) to kilometers per second (km/s), you need to understand the breakdown of time units. Every hour contains 3,600 seconds (because there are 60 minutes in an hour and 60 seconds in each minute). Thus, converting involves dividing the speed in km/h by 3,600 to calculate how much distance you cover in each second.For example, let's consider a speed of \(60.0 \, \text{km/h}\):\[\frac{60.0 \, \text{km/h}}{3,600 \, \text{s/h}} = 0.0167 \, \text{km/s}\]**Conversion Steps:**

• Take the speed in kilometers per hour.
• Divide by 3,600 to convert to kilometers per second.
• Your result is the speed per second.