Control Time-remapping with expression

The value an expression generates for the time remapping property is time in seconds. If you just type a number in you get whatever the Time indicator is set to. Set the time indicator to frames and type in 40 and you'll get 40 frames, Change the Time indicator (Ctrl/Cmnd + Click) to timecode in a 30 fps comp and the display will read 0:00:01:10. 

Add an expression and type in 1.5 and you'll get 45 if the 30 fps comp is set to frames, but change the display to Timecode and you'll get 0:0:01:15. 

If you want to jump to 10 seconds then just multiply the slider value by 10. If you want to make sure that it is exactly 10 seconds then add Math.floor(slider value) so you don't get any frames between the sections and multiply that by 10. Math floor will keep the time from advancing to the next 10 seconds until the next whole number is generated by the slider. That expression would look like this:

sectionID = effect("Slider Control")("Slider");
Math.floor(sectionID) * 10;

If you want the section to play from its starting point and not continue past the endpoint of the animation then you need to have every animated section be the exact number of frames you want to play, then complicate the expression by finding the time value of the keyframe for the slider, and only allowing the time value to increase by 1 frame until the frame count is one less than 10 seconds. I would need AE open to write that expression and be confident in making it work for you, but the idea is to find the time of the nearest slider keyframe, then allow the frame count to move up at the rate of one frame per comp frame until the count is 1 frame less than 10 seconds, then hold on that frame. 

Is this slider going to be animated, so that at each slider keyframe you want the corresponding section to begin, or is it a static control? What should happen when it gets to the end of the section?