When you are doing repetitions to a new maximum number, let's say going from 25 to 50 situps, it can be daunting both physically and psychologically.

To get past the psychological barrier, I'll do the 25 situps that I know I can do but then
instead of counting to 50, I'll say to myself, "Can I do 10 more?". I'll say yes and do those 10.
Chances are those 10 were hard but that still leaves 15 more to do. I'll ask myself again but this time, the question is "Can I do 5 more?". I'll say yes and huff and puff to do another 5. 10 more to do and the question becomes "Can I do 2 more" each time for 5 times until I hit 50. An each of those 2 situps will be a lot slower but I know in my head I can do 2 situps.

When there is a psychological barrier of making a large leap, break it down into smaller components to get there.