
Make an arc, convert it to Bezier curve with Path > Object to Path
insert the wanted stroke width
Insert the breaking points with the node tool (=double-click) and break the curve at those points. Make the pieces separate by applying Path> Break Apart and insert the wanted stroke colors
Select all, apply Path > Stroke to Path to get filled areas that can have an outline stroke. Here a black stroke is selected
Another way: Divide your closed path (made by applying stroke to path) to separate colorable areas. Draw a radial line over it, select both and apply Path > Division.
You need as many radial lines as there's division points. Start the lines from the center of the arc. To find the centerpoint easily draw at first a circle.
3rd way: Draw the scale as horizontal rectangles, select them and apply Path > Combine to get a combined path which behaves like a single path.
Combined path can have only one color, but it can have text parts which are converted to paths
Copy the combined path to the clipboard. Insert path effect Pattern along Path to your arc. The arc must be converted to Bezier curve with Path > Object to Path before it accepts path effects.
The effect dialog has icon Paste Path to take the pattern from the clipboard:

You must apply Path > Object to Path and Path > Break Apart to get freely colorable areas.