In to go bet. (Prof. Skeat takes it as = go better, i.e. go quicker.)

transitive. to mend one's pace: to travel faster; (also) to adjust one's speed, esp. to match a companion, etc.

intransitive. To become faster; to be accelerated.

Of a ‘pace’: To increase, be quickened.

intransitive. To begin to move more quickly, to increase in speed; (Physics) to change in velocity.

intransitive. To become swift or swifter; loosely, to move swiftly, hasten, hurry.

to step on (hit,etc.) the gas: to cause a motor vehicle to accelerate by depressing the accelerator pedal (frequently figurative or in figurative…

Chiefly British and Australian colloquial (originally Military slang) to pull one's finger out and variants: to stir oneself to action; to stop…