Arc Length Units: Explained & Solved Problem

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The arc length for a circular segment can be calculated using the formula arc length = radius * angle. In this case, if the velocity is measured in meters per second (m/s) and time in seconds (s), the arc length is expressed in meters. Although radians are dimensionless, they are used in the formula, leading to the conclusion that the units for arc length remain meters. Therefore, regardless of the initial confusion, the unit of arc length derived from the given graph is ultimately meters. Understanding these relationships clarifies the measurement of arc length in physics.
alingy2
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Hello,

I solved the arc length for a particular problem. However, what is the unit of arc length if the units of the velocity vs time graph are m/s vs s?

I am really confused.
 
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Well, suppose you wanted to know the arc length of a portion of a circle; the typical formula is arc length = radius*angle. So the units would be meters*radians in standard SI. Although radians is a dimensionless unit, so you could also say units are just meters.
 

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