1) Runners sped up on the track.
2) There's a little boy in the field.
However, #2 could go either way. If it is a field of flowers, then I would say "in the field". However, if it is a baseball field then I would say "on the field". But just to make it more confusing, for sports fields sometimes we say "he is in the field of play".
I hope that helps :)