THESAURUS
push on
accelerate, bundle, bustle, chase, crowd, dash, dash off, dash on, dispatch, double-time, drive on, expedite, fare, festinate, forge ahead, forward, get going, get moving, go, go slow, haste, hasten, hasten on, hie, hie on, hurry, hurry along, hurry on, hurry through, hurry up, hurry-scurry, hustle, hustle up, inch forward, journey, leap, lose no time, make haste, move quickly, muddle through, pass, plunge, post, precipitate, press, press forward, press on, proceed, process, push, push forward, push through, quicken, race, railroad through, repair, run, rush, rush along, rush through, scamper, scramble, scurry, scuttle, speed, speed along, speed up, spur, spurt, stampede, tear, travel, urge, wend, whip, whip along
ROGET THESAURUS
push on
Haste
VB
haste, hasten, make haste, make a dash, hurry on, dash on, whip on,
push on, press on, press forward, hurry, skurry, scuttle along, barrel along, bundle on, dart to and fro, bustle, flutter, scramble, plunge, plunge headlong, dash off, rush, express, bestir oneself, lose no time, lose not a moment, lose not an instant, make short work of, make the best of one's time, make the best of one's way, be precipitate, jump at, be in haste, be in a hurry, have no time, have not a moment to lose, have not a moment to spare, work against time, quicken, accelerate, expedite, put on, precipitate, urge, whip, railroad.
Progression
VB
advance, proceed, progress, get on, get along, get over the ground, gain ground, forge ahead, jog on, rub on, wag on, go with the stream, keep one's course, hold on one's course, go on, move on, come one, get on, pass on,
push on, press on, go forward, move forward, come forward, get forward, pass forward, push forward, press forward, go forwards, move forwards, come forwards, get forwards, pass forwards, push forwards, press forwards, go ahead, move ahead, come ahead, get ahead, pass ahead, push ahead, press ahead, make one's way, work one's way, carve one's way, push one's way, force one's way, edge one's way, elbow one's way, make progress, make head, make way, make headway, make advances, make strides, make rapid strides, go ahead, shoot ahead, distance, make up leeway.