How to Find an Average Rate of Change
Know the formula for calculating average speed., Determine the starting position., Measure the distance to the endpoint., Measure the elapsed time., Calculate the average speed., Convert the units as necessary.
Step-by-Step Guide
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Step 1: Know the formula for calculating average speed.
Suppose you want to know the average speed of travel, but you do not have a speedometer.
It is possible to calculate speed with some basic measurements and calculations.
The average speed of any object is found by dividing the change in position by the change in time.
This can be written mathematically as:speed=ΔxΔt{\displaystyle {\text{speed}}={\frac {\Delta x}{\Delta t}}} In this function, Δx{\displaystyle \Delta x} represents the change in position or the distance traveled.
The denominator Δt{\displaystyle \Delta t} represents the change in time. -
Step 2: Determine the starting position.
Average speed of an object is is the calculation of its change in position, or location, over a chosen period of time.
Therefore, to begin, you need to select the starting position for your measurement.For example, if you want to measure your average walking speed from your house to your school across town, the starting position is your house.
The “starting” position does not have to be a true start.
For example, you could choose to measure the average speed of a race car in the Indy
500.
You might select any point along the track as the “starting” point for your measurement. , You can calculate the average speed over any distance or length of time that you choose.
The only limiting factor is the quality or precision of your measuring instrument.
For example, measuring the speed of a sprinter requires accuracy within a few centimeters, while measuring the speed of a race car needs to be accurate to within a few feet or meters.To measure your walking speed from home to school, you could find the distance either by looking at a local map, or by traveling the route with a car’s odometer.
For this example, assume that the distance is
0.6 miles.
For the Indy 500 race car, one lap of the Indianapolis Speedway race track is
2.5 miles.
Therefore, check the car’s position at any point on the track.
When the car passes that same point again, it’s distance will be
2.5 miles. , The average speed requires you to measure the amount of time that goes by.
As with the distance measurements, this may require more of less precision, depending on the speed itself.
For example, you need a stopwatch that measures tenths or hundredths of seconds to measure the speed of world-class sprinters, but a regular watch with a second hand can measure the speed of a race car around a track.For the walking trip to school, you can probably use a wristwatch to measure the time.
Suppose, for this example, that the walk to school takes fifteen minutes.
Watching the race car around the Indianapolis Speedway, you can time each lap with a watch or stopwatch.
A fast car will take about 45 seconds to complete one lap. , After you have taken the measurements that you need, you then simply place them into the formula for speed calculation to find the speed of the object.
Pay attention to the units that you use for the calculation.For the walking trip to school, the distance was measured at
0.6 miles, and the time was fifteen minutes.
Place this information in the formula as follows: speed=ΔxΔt=0.615=0.4{\displaystyle {\text{speed}}={\frac {\Delta x}{\Delta t}}={\frac {0.6}{15}}=0.4} miles/minute.
The Indy race car traveled
2.5 miles in 45 seconds.
This data goes into the formula for speed calculation as follows: speed=ΔxΔt=2.545=0.0556{\displaystyle {\text{speed}}={\frac {\Delta x}{\Delta t}}={\frac {2.5}{45}}=0.0556} miles/second. , Sometimes, the final calculation may not be in the units that are most useful to you.
If you need or wish to report the speed in different units, you will need to multiply by some conversion factor.
For example, a race car’s speed is generally measured in miles per hour, not miles per second.
Because one hour is equal to 3600 seconds, you can convert the calculated speed by multiplying by 3600 seconds per hour.0.0556 miles per second∗3600 seconds per hour=200.16 miles per hour{\displaystyle
0.0556{\text{ miles per second}}*3600{\text{ seconds per hour}}=200.16{\text{ miles per hour}}}. -
Step 3: Measure the distance to the endpoint.
-
Step 4: Measure the elapsed time.
-
Step 5: Calculate the average speed.
-
Step 6: Convert the units as necessary.
Detailed Guide
Suppose you want to know the average speed of travel, but you do not have a speedometer.
It is possible to calculate speed with some basic measurements and calculations.
The average speed of any object is found by dividing the change in position by the change in time.
This can be written mathematically as:speed=ΔxΔt{\displaystyle {\text{speed}}={\frac {\Delta x}{\Delta t}}} In this function, Δx{\displaystyle \Delta x} represents the change in position or the distance traveled.
The denominator Δt{\displaystyle \Delta t} represents the change in time.
Average speed of an object is is the calculation of its change in position, or location, over a chosen period of time.
Therefore, to begin, you need to select the starting position for your measurement.For example, if you want to measure your average walking speed from your house to your school across town, the starting position is your house.
The “starting” position does not have to be a true start.
For example, you could choose to measure the average speed of a race car in the Indy
500.
You might select any point along the track as the “starting” point for your measurement. , You can calculate the average speed over any distance or length of time that you choose.
The only limiting factor is the quality or precision of your measuring instrument.
For example, measuring the speed of a sprinter requires accuracy within a few centimeters, while measuring the speed of a race car needs to be accurate to within a few feet or meters.To measure your walking speed from home to school, you could find the distance either by looking at a local map, or by traveling the route with a car’s odometer.
For this example, assume that the distance is
0.6 miles.
For the Indy 500 race car, one lap of the Indianapolis Speedway race track is
2.5 miles.
Therefore, check the car’s position at any point on the track.
When the car passes that same point again, it’s distance will be
2.5 miles. , The average speed requires you to measure the amount of time that goes by.
As with the distance measurements, this may require more of less precision, depending on the speed itself.
For example, you need a stopwatch that measures tenths or hundredths of seconds to measure the speed of world-class sprinters, but a regular watch with a second hand can measure the speed of a race car around a track.For the walking trip to school, you can probably use a wristwatch to measure the time.
Suppose, for this example, that the walk to school takes fifteen minutes.
Watching the race car around the Indianapolis Speedway, you can time each lap with a watch or stopwatch.
A fast car will take about 45 seconds to complete one lap. , After you have taken the measurements that you need, you then simply place them into the formula for speed calculation to find the speed of the object.
Pay attention to the units that you use for the calculation.For the walking trip to school, the distance was measured at
0.6 miles, and the time was fifteen minutes.
Place this information in the formula as follows: speed=ΔxΔt=0.615=0.4{\displaystyle {\text{speed}}={\frac {\Delta x}{\Delta t}}={\frac {0.6}{15}}=0.4} miles/minute.
The Indy race car traveled
2.5 miles in 45 seconds.
This data goes into the formula for speed calculation as follows: speed=ΔxΔt=2.545=0.0556{\displaystyle {\text{speed}}={\frac {\Delta x}{\Delta t}}={\frac {2.5}{45}}=0.0556} miles/second. , Sometimes, the final calculation may not be in the units that are most useful to you.
If you need or wish to report the speed in different units, you will need to multiply by some conversion factor.
For example, a race car’s speed is generally measured in miles per hour, not miles per second.
Because one hour is equal to 3600 seconds, you can convert the calculated speed by multiplying by 3600 seconds per hour.0.0556 miles per second∗3600 seconds per hour=200.16 miles per hour{\displaystyle
0.0556{\text{ miles per second}}*3600{\text{ seconds per hour}}=200.16{\text{ miles per hour}}}.
About the Author
Robert Anderson
Robert Anderson has dedicated 3 years to mastering lifestyle and practical guides. As a content creator, Robert focuses on providing actionable tips and step-by-step guides.
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