Caffeine Bullet Time is when a hyperactive character of some sort, usually a comic Side Kick, ends up saving the day by increasing their speed to superhuman levels with some sort of stimulant. Coffee, sugar, drugs, whatever the source, sometimes the speed increase is so great that it seems like Time Stands Still. Since this is a comedy trope, the stimulant is usually caffeine.
In some cases, it is a generally low-Genki character who imbibes enough caffeine to send them into bullet time.
Of course, despite caffeine being a G-Rated Drug, caffeine overdose in the real world is not pretty. Wikipedia claims it can cause "dizziness, fast heartbeat, blurred vision, drowsiness, dry mouth, flushed dry skin, increased urination, loss of appetite, nausea and stomach aches". Consume "enough" at one time and it will kill you; for example, if you could drink about 154 cans of Mountain Dew in five minutes, you wouldn't be around to finish number 155. (Of course, your stomach would burst long before the caffeine did you in. However, this is a real hazard with caffeine pills; you can kill yourself by popping too many.) And, unlike more controlled stimulants, it has an obnoxiously narrow effective range, which commonly involves toeing the superthin line between still barely feeling it and side effects already present in force, even for a heavily dependent Caffeine Junkie (not an exaggeration in the least, as caffeine withdrawals have pronounced physical symptoms, and last far longer than most any "real" drug... As ubiquitous an ingredient as it is, most heavily dependent persons in modern societies just rarely experience going entirely without it long enough for full-force physical WDs to kick in, and would almost never end up in a situation where they could, much less actually would ride them out cold turkey until they subside.)
It certainly doesn't make time appear to stand still around you in a hyper-stimulated Bullet Time (although some people have reported a short period of "everything going slowly" right before crashing). But this is Comedy Land.
Usually used in cartoons.
In the Harry Potter / Justice League crossover Terminal Justice, after drinking fourteen pots of iced mocha, Harry started skipping down the hallway singing and babbling a mile a minute and was described by the author as "greatly resembling Flash on a sugar high".
In Growing Up Kneazle, after spending nearly his entire pre-Hogwarts childhood in his Kneazle animagus form, Harry discovered that in human form, catnip had a stimulant/hallucinogen effect on him.
In the live-action George of the Jungle film, George sees a commercial for "Chock Full o'Nuts" coffee which suggests that drinking coffee will stimulate a romantic relationship. He proceeds to get the can from the pantry and eat the grounds. Cue several minutes of him running around the apartment at top speed, acting insane and chanting "Javajavajavajavajavajavajavajavajavajavajava..."
Played straight in Over the Hedge. In the climactic fight between the woodland dwellers and the suburbanites, Verne and RJ give Hammy, the hyperactive squirrel, an energy drink. He enters Bullet Time and leisurely strolls past the exterminator, a crazy happy dog and the crazy House Wife to activate the laser grid defense system, while getting the cookie he wanted earlier to boot. Not only that, when he activates the lasers, he casually walks past the slowly extending beams, which means he exceeded the speed of light. He had enough time left to forage for an empty log's worth of food.
The movie Hoodwinked also included a hyperactive squirrel (named Twitchy) who, at the end, needed a caffeine boost to rocket down a mountain to warn the cops about the Big Bad while the rest of the cast tried to stop his evil plot. Unfortunately, when the squirrel finds the cops, he spoke so fast that they couldn't understand a word he said (similar to how Mumbles's testimony was portrayed in the movie Dick Tracy).
The cops then recorded him repeating his superspeed speech, and played it back at about half- or quarter-speed, which gave him a very *deep* , smooooooth voice resembling an automated phone recording. This is a parody of how most people sound awful on tape, but Twitchy sounds very cool and collected. He actively preens himself as he hears the recording.
The 2000 short film Sixty Cups of Coffee has the main character explain to the audience that drinking sixty cups in a single sitting allows the drinker to "see the truth", although what that truth could be is left unclear. The short centers on this character slamming cup after cup, the diner patrons having varied reactions to his attempt: the waitress worries for his health, the mother tells her curious son to look away, the truckers betting increasing amounts of personal trinkets over his success or failure and so on. Something happens after the 60th cup but the ending is left open to interpretation.
Live Action TV
This happens to Manny in Black Books when Bernard gets him an espresso machine and a cop series boxset for his birthday.
In one episode of Outnumbered, the already-hyperactive Ben and his older and more responsible brother Jake (who is not responsible on this occasion) drink (black?) coffee and their mom is devastated when she learns about it, because she'll have to deal with even more outrageous behaviour than usually.
In the "Wink of an Eye" episode of Star Trek, Deela slips Kirk a drug which speeds him up to Bullet Time, enabling him to see her and her compatriots who live in Bullet Time permanently. But since she got the drug into him by slipping it into his coffee, it ends up looking an awful lot like Caffeine Bullet Time.
Averted in an episode of Voyager. Captain Janeway refuses a cup of coffee with the comment, "One more cup and I'll go to warp."
Dilbert. Wally teaches Dilbert that "sadness is another word for not enough coffee". As a result of the massive coffee cup Dilbert begins carrying around, he completes all his projects in a day before developing X-ray vision, precognition, and telekinesis. Unfortunately, just as he's telekinetically crushing the PHB's throat a la Darth Vader, he wakes up.
In Helen, Sweetheart of the Internet, Helen and her friend are at a coffee shop, and Helen orders some sort of boosted, experimental coffee. After remarking that she doesn't seem to feel the supposed effects of all this extra caffeine, she stands up and notices that her friend is in the middle of a blink, and that she has gone into Caffeine Bullet Time.
The Mage: The Ascension had the Technocracy bring out a little gem in the form of caffeine plus: "You'll be so wired, you'll see into other dimensions. Any more caffeine and you'll start vibrating off sound waves. Caffeine plus is dangerous to the human body, addictive to the mind, poisonous to the soul and sheer heaven with a pack of smokes."
When she realizes how little she has to show for her time as a Congresswoman, she does this deliberately to ensure she has a legacy. When she comes down, Community is America's top comedy, Transformers Animated is in its fourth season, Justin Bieber is in line for the Nobel Peace Prize, and WORLD PEACE has been declared. Unfortunately, this all comes at the cost of her relationship with Leslie. And the World Peace is later overturned because it's bad for war industries.
Agatha Heterodyne in Girl Genius. She drinks a cup of coffee (apparently her first ever), then she asks for a book on coffee, gets the book, reads the book, marks all the spelling errors in the book, comprehends the material, and rushes off for ingredients. All before the waitress can finish her answer. She then proceeds to disassemble and reassemble a broken coffee machine, fixing it and making it capable of making the most spectacular coffee ever.
Kiki, the ferret mascot in Sluggy Freelance, goes into hyperspeed whenever she eats candy. This has actually been used as an offensive technique by the protagonists of the comic, after they notice that this state allowed her to break through concrete walls due to sheer propulsion with apparently no damage to herself.
Despite some claims about Truth in Television, this can actually have the opposite of the intended effect. CNS stimulants like caffeine tend to increase the mind's obsessive-compulsive-perfectionist tendencies and make reaction times worse, whereas a light alcohol buzz will make players more relaxed and less hesitant (and, paradoxically, stimulate some parts of the brain due to alcohol's effect on glutamate receptors), thus improving reaction time. Reaction time is worthless if you can't aim well.
A modified version shows in the Rooster Teeth staff comics (featuring a fan drawing comics of the staff who brought us Red vs. Blue). The mellow Matt Hullum is shown often drinking coffee, but laid back. Someone tries swapping in decaf. The next scene shows that were Matt any more mellowed out, he'd be dead.
That's not a fan, that's Geoff Ramsey's wife. Matt Hullum probably does drink that much coffee.
From the Global Guardians PBEM Universe, Mister Excitement was a member of the Crimestoppers a team of superhero wannabe's. Excitement had honest to God super-strength and Super Speed... except he gained the super-strength by way of adrenalin rushes, and there was never a guarantee he was going to have one. Mister Excitement was hyper-active, fidgeted, and his team instinctively knew that whatever they did, giving this man caffeine was a bad thing because who knew what would happen. But when the chips were down and they were captured by a real supervillain, they consciously invoked this trope, allowing Mister Excitement to save the day.
From SCP Foundation. SCP-914's outputs when the input was a Red Bull. On "Fine" setting the output "Red Bull Ultra" let the subject be awake for 3 days straight with no ill effects. The "Very Fine" output? "Security on duty reported seeing 'some kind of gray blur'."
Das Bo Schitt's Update Day revolves around Heavy consuming a "Bonk! Atomic Punch" and a sandvich, causing a thermonuclear reaction in his stomach to such levels that time slows nearly to a halt. He then sets out and causes everything shown in the beginning sequence, which includes switching Medic's medic-gun with Soldier's bazooka, shoving Demoman's grenade launcher down his throat, lightly punching Sniper's head, which would be enough force in real time to send his head flying, then gets a massive diarrhea attack because of the drink/sandwich mix. While on the run, he rapid-fire punches Rochelle to the ground, grabs the portable toilet she was waiting for, runs back to base, stopping to startle Soldier with garbled speech, then puts down the toilet and uses it. Pyro spots both him and Spy, and because of the reeking gasses from Heavy, the whole building explodes when Pyro starts his flamethrower.
Strong Bad slips Strong Sad some caffeine in one of the Homestar Runner Strong Bad Emails. Strong Sad, normally a very sedate Eeyore, starts twitching madly and yelling incoherently about "Wood-davers! Wood-davers! Sell 'em at the corner store, sell 'em at the five-and-dime!" and slapping Coach Z until the Coach protests "Stop it! I don't wanna die!"
In RWBY, the history professor Bartholomew Oobleck is in a constant state of this, as implied by his rapid dashing.
Futurama has this in the episode "Three Hundred Big Boys", where all the characters get a $300 refund and Fry decides to spend his on one hundred cups of coffee. His caffeine addiction grows stronger with each cup he drinks, twitching and babbling his way through the episode. Towards the end, all the characters are trapped in a burning building, but Fry is too overdosed to notice and throws back his hundredth cup. Time slows to a crawl for him, and he appears to have achieved caffeine enlightenment as he serenely carries everyone out of the building and puts out the fire. Leela remarks that she thinks they were saved by "a mysterious, orange blur".
In one Earthworm Jim episode, Psycrow develops this sort of power after drinking ridiculous amounts of espresso, becoming "Hyper Psycrow". Jim, in turn, counters him by becoming "super-mellow" through the use of an aromatherapy kit (one was hung on this, as Peter questioned how a worm without a nose could use the kit). When they touch, the universe explodes.
In Avatar: The Last Airbender , an Earth Kingdom general is trying to artificially induce the Avatar State in Aang and at one point feeds him their world's equivalent of Red Bull. It just turns him into even more of a Keet.
In the movie The Iron Giant, young protagonist Hogarth Hughes pays a late-night visit to beatnik junk artist Dean, who is drinking espresso. Hogarth asks for some, insisting he can handle it despite Dean's warning that the drink is "like Coffeezilla." Quick-cut to the rapid speech, wild gesturing, shaking hands... asking for more espresso...
In the Family Guymovie, there's a scene of Stewie driving an RV offroad in Nevada while wired on caffeine pills, yelling about being like "the pioneers, man!" He promptly crashes, and while Stewie doesn't seem to notice at first, as soon as the airbag deploys as a makeshift pillow, he falls asleep.
In a later episode, after Peter is introduced to Red Bull by Quagmire. He becomes addicted to it and becomes this for the first act of the episode
Spliced: Peri experiences this as a result of consuming huge amounts of sugar in "Sugar Low".
In one episode of Regular Show, Mordecai and Rigby end up buying double-glazed fritter donuts. Pops eats one and starts experiencing a sugar rush. Skips says that the only way to calm him down is to make him crash, by consuming MORE SUGAR. Mordecai, Rigby, and Skips each eat a fritter themselves just to put them on the same level as Pops, but then the world started slowing down around them. Skips recommended to consume even MORE sugar. Pops, Rigby, and Mordecai started moving so fast that the world around them started to break down. Physics, Time, Colors, the world started looking like an Eldritch Location.
An unhealthy amount of caffeine (consuming several energy drinks or a large amount of coffee in quick succession) can lead to the feeling of heightened senses or slowed down time/sped up reaction, though nothing like it is portrayed in fiction similar to adrenalin, as explained below. It's not recommended for health reasons (sugar content, inability to sleep) especially given that people have died from drinking Monster drinks, and the trade off being once the caffeine or rather sugar rush wears off the body essentially crashes, making this a very real and dangerous case of Phlebotinum Overload. If you really want the effects of this then foods high in dopamine or supplements are a much milder yet safer alternative.
There have been scientific experiments which indicate that when pumped on adrenalin, perception of the world slows down sufficiently to see numbers flashing between black on red and red on black too fast for normal human perception to read. Also, experiments done on mice indicate that their perception slows down sufficiently so that they're off by about four seconds too soon while on speed when trained to push a button after ten seconds.
There was once an interview with a member of a SWAT team who during a fire fight noticed these cans floating in front of him with government stamped bottoms. He later realized that he was so hopped up on adrenaline that he was able to read the bottoms of the cartridges his gun was ejecting at a time.
A combination of this effect and extremely keen eyesight allegedly allowed Ted Williams to watch the seams on baseballs rotate as they hurtled towards him when he was batting.
Amphetamine, which (to a first approximation) mimics adrenaline, can have the same sort of effect, for example making it easier to swat flies with your bare hand as it becomes possible to see them taking off as your hand approaches and correct your trajectory to compensate.