"The table shows how far Object 1 traveled as a function of time.
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Time (sec)| Distance Traveled (ft)
x | y
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2 | 18
4 | 36
6 | 54
8 | 72
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The equation shows how far Object 2 traveled in feet as a function of time in minutes.
f(x) = 10x
Which object traveled at a faster speed? Justify your response.
WARNING: Object 1 is in Feet per Second and Object 2 is in Feet per Minute, you will need to convert them so they are in the same units before comparing them."
Help please?
Object 1 travels 9 feet per second.
Object 2 travels 10 feet every 60 seconds.
To compare the speed of Object 1 and Object 2, we need to convert their units to the same unit of measurement.
First, let's convert the units of Object 1 from feet per second to feet per minute, which is the unit of measurement used for Object 2.
In 1 minute, there are 60 seconds. So, to convert from feet per second to feet per minute, we need to multiply the distance traveled by Object 1 by 60.
Let's calculate the distances traveled by Object 1 for all the given time values and convert them to feet per minute:
For Object 1:
Time (sec) | Distance Traveled (ft)
2 | 18 ft/s * 60 = 1080 ft/min
4 | 36 ft/s * 60 = 2160 ft/min
6 | 54 ft/s * 60 = 3240 ft/min
8 | 72 ft/s * 60 = 4320 ft/min
Now, let's compare the distances traveled by Object 1 and Object 2 at the same time values. Since they now have the same unit of measurement (feet per minute), we can directly compare the distances.
Comparing the distances at Time = 2 minutes:
Object 1: 1080 ft/min
Object 2: f(2) = 10 * 2 = 20 ft/min
Comparing the distances at Time = 4 minutes:
Object 1: 2160 ft/min
Object 2: f(4) = 10 * 4 = 40 ft/min
Comparing the distances at Time = 6 minutes:
Object 1: 3240 ft/min
Object 2: f(6) = 10 * 6 = 60 ft/min
Comparing the distances at Time = 8 minutes:
Object 1: 4320 ft/min
Object 2: f(8) = 10 * 8 = 80 ft/min
From the comparison, we can see that at every time value, the distances traveled by Object 2 (using the equation f(x) = 10x) are greater than the distances traveled by Object 1 (after converting from feet per second to feet per minute). Hence, we can conclude that Object 2 traveled at a faster speed.