Green’s Dictionary of Slang

1. (drugs) to use amphetamines or similar ‘go-faster’ drugs [speed n. (6)].

1971		E.E. Landy Underground Dict. (1972).
1980		E. Folb Runnin’ Down Some Lines 186: You get a young lady to speed, get her loaded.
1989		(con. 1950s–60s) in G. Tremlett Little Legs 170: When they’re speeding, they [...] don’t know what day it is.
1999		K. Sampson Powder 92: He’s been drinking nothing but coffee and water for two hours. He’s speeding his nuts off. He’s raring to go.
2000		Observer Mag. 25 Jan. 32: I was speeding out of my head one night.
2017		A. Parks Bloody January 80: Sitting in an after-hours club speeding out his mind.

2. (US campus) to work very hard, esp. when preparing for a test or examination; thus speeding n. [SE speed].

1982

W. Safire What’s The Good Word? 301: New terms for ‘cramming’ are ‘shedding’ (from ‘woodshed’), ‘speeding,’ and ‘heavy booking’ or ‘mega-booking.’.

3. fig. use of sense 1, to feel energized in a similar way to the above, but without the use of drugs.

1999

K. Sampson Powder 357: Everyone was hyped up, still speeding from the show and Wheezer’s fantastic news over breakfast.