So there's this character who can go fast. Really fast. So fast in fact, that they couldn't quite stop in time. It may be because they're going a lot faster than they usually go. It may be because the speed is due to a recent upgrade. It may be because the character only knows how to go fast but never bothered to learn how to brake.
Whatever the reason, the results are the same. Spectators wincing in empathy as the speedster crashes or suffers something just as painful.
When a character invokesToo Fast to Stop to cause someone else to crash, it's the Wronski Feint. This is one of the reasons why the Door Judo works. Some Bullfight Bosses can be like this. Compare with Inertia Is a Harsh Mistress.
Often a subtrope of Required Secondary Powers, see that trope for other examples of superpowers being trumped by physics — Including the other obvious Super SpeedRequired Secondary Powers: The ability to react fast enough to control yourself in super speed, the toughness required to keep your feet from turning into bloody stumps at 250+ MPH, skin that can survive the heat from the air friction, etc etc.
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Anime and Manga
During their B-Rank promotion test in Magical Girl Lyrical Nanoha, Teana piggy-backed on Subaru while the latter roller-bladed to the finish line at full speed. Teana then asked the dreaded question on how they were supposed to stop. Cue looks of horror as they headed straight to a barricade. They escape almost unharmed thanks to their examiners/instructors' intervention but fail the test.
An earlier occurrence of this same example takes place in Ranma 1/2's Martial Arts Ice Skating duel. After tossing Akane into the air and punching Mikado while skating past him, Ranma catches Akane on his back and... continues forward at full speed. He can barely skate as it is, and both Ranma and Akane scream as they're about to smash into the wall. Somehow, he manages to flail his feet upwards and wall-climb a few seconds to kill off the momentum, then flips back on his feet. The horror still frozen on their faces betrays how improbable this recovery was.
The first episode of Moldiver had a rather prolonged scene with the main character running at supersonic speeds, tripping, and skidding along the ground for long enough to more or less destroy an entire race track. Come to think of it, this was pretty much the #2 go-to gag of the series behind crossdressing.
Captain Kuro of One Piece is an interesting case while using his Shakushi attack. He seems to be perfectly capable of stopping himself whenever he wants (though we never see it because Luffy always manages to stop him first), but the attack makes Kuro too fast to see where he's going or who he's attacking, so he's basically "Too Fast To Know When To Stop".
In Katekyo Hitman Reborn!, Tsuna suffers from this right off the bat when his gloves updated to Ver. VR. This resulted in zooming past his ridiculously bloodthirsty oponent and running into cement-reinforced walls, therefore resulting in a curb stomp.
In the Fullmetal Alchemist manga, Sloth is very easy to set traps for: you just get out of the way when he charges ludicrously fast, and he'll run straight into whatever was behind you. Just make sure you're not in-between or you won't exist any longer.
Used in one battle of Mahou Sensei Negima!. Takahata Takamichi explains that the weakness of the series' version of the Flash Step is that once you enter it, you can't stop until you reach your destination, and proving it by tripping Negi as the kid tries to Flash Step past him.
Also stated to be a big weakness of the "Raiten Taisou" lightning-form Negi comes up with in the Magical World: yeah, he can move at the speed of lightning, but his perceptions aren't enhanced, so he can't react quickly enough to change direction mid-flight, making him an easy target for someone skilled enough to guess where he's going. Then Negi reveals "Raiten Taisou 2", which corrects this problem.
In Darker Than Black, a Contractor named Goran has this problem. He has super speed, but moves in short bursts almost to the point of FlashStepping because of difficulty stopping and turning. This causes him to run into things and is responsible for his death. Earning him the Fan Nickname of "Russian Burger Flash Running Into Trees". Due to his country, remuneration, power, and being Too Fast to Stop.
In Smile Pretty Cure, when Nao first becomes Cure March, she ends up learning (accidentally) she has super speed... by accidentally racing past Akaoni and slamming face first into a bridge truss. She ends up stepping out of the imprint she left rather unharmed and she was more confused than anything.
Naruto, in his Kyuubi Chakra Mode, ambushes Kisame so hard that his foot gets stuck in the wall and he wrecks his ankle.
A Calvin and Hobbes strip had Calvin roller-skating down a hill and not knowing how to stop. Of course, taking that suggestion from Hobbes about steering into a gravel driveway wasn't all that helpful.
Calvin and Hobbes did this sort of thing all the time—with sleds by winter and a red wagon by summer. It usually provided an action backdrop to avoid "talking heads" in a deeply philosophical discussion... And the inevitable crash at the end provided a nice counterpoint. On a few memorable occasions, the entire discussion was about the impending crash.
Jason Fox and his best friend Marcus have had several sledding adventures similar to Calvin's.
The Flash has been known to use this in order to defeat rival speedsters. He also falls prey to it himself whenever it's time for him to job for someone who should have no realistic way of beating him, despite his Super Reflexes.
Mina Mongoose of the Sonic the Hedgehog comic series suffered from this initially, thus forcing her to ask Sonic to help. She also used those moments to try and win his heart.
Angel/Archangel of the X-Men often performs an aerial variant on his enemies. Specifically, Archangel isn't nearly as fast as most airborne people in the Marvel Universe, but he is far more agile, and sometimes it's hard to see the incoming wall with those big wings in your vision...
Scott Pilgrim: The cause of Lucas Lee's demise when Scott dares him to skateboard grid down a long flight of steps. Lucas accepts the challenge but the speed is too much for him. And he can't dismount in time when he reaches the bottom, exploding as a result. The caption even lampshades it as "Too Fast To Live".
In the second The Mighty Ducks film, a speed skater (Luis Mendoza) was introduced into the team. He was extremely fast and actually quite agile and maneuverable, but he had one slight problem... which was shown when he "stopped" by hitting the boards with a splat.
In Spaceballs, Dark Helmet orders that his ship be put to "Ludicrous Speed" to capture the fleeing heroes. However it proves to be too fast and they overtake them. Helmet then orders his right hand man to stop the ship, ignoring all warnings that they need to slow down first. The result is that he gets thrown head-first into a computer console.
The first Flash movie has the titular protagonist find out he has super-speed in a rather unexpected way: he starts chasing after a bus, then overtakes it, and soon enough he's hurtling through the city, unable to stop. He only stops when he hits the sea, and the water finally kills his momentum.
In Titanic Captain Smith ordered the last boilers lit on Bruce Ismay's insistence, so the ship was going full steam ahead when the iceberg was spotted right in its path. The crew threw it into full reverse, but it had far too much momentum to stop and a rudder far too small to turn it in time. The rest is history.
In X-Men: The Last Stand, Kitty Pryde is getting Juggernaut to chase her through the walls of the Alcatraz laboratory, right up to the room where Leech is. Since she can't phase anymore, she moves close to the far wall and when Juggernaut comes bursting through the last wall, he runs full steam towards them. Unfortunately for him, Leech's power kicks in and he slams into, not through, the wall with enough force to knock himself out.
The Ambiguous Puzuma of Discworld is the fastest animal on the Disc, achieving near light-speed (which isn't too hard, given the low speed of light on the Disc). While they can never be seen, their remains are occasionally found on cliffs and large rocks. These show a black-and-white checked coat and a thin, flat shape.
This happens to a kangaroo when a transportation spell goes wrong at the end of Interesting Times. The wizards have never seen one before, conclude that it's a giant rat and wonder if it's naturally one inch thick and deep-fried.
In The Last Continent, Lovable Coward Rincewind is suddenly told he's running towards the danger and tries to stop, but "his method of running was very efficiently based on the idea that stopping was the last thing he'd do."
From the original Tales of Munchausen, there was a man who was so fast, he had to tie heavy weights to his legs just to run at a useable speed - otherwise, the first step he takes, he'd stumble and fall over the equator.
One of the Drizzt books had him facing a drow warrior with enchanted bracers that made his arms move impossibly fast. Unfortunately, he'd apparently never really learned to fight with them, so his footwork and other positioning suffered, and his arms moved too fast for him to stop a move he'd started. Drizzt killed him and took the bracers...and after figuring out that even with his training he couldn't overcome the drawbacks, lamenting that a warrior wins with his feet, not his hands. So he put them around his ankles.
Live Action TV
The first season episode of Heroes with Nathan landing outside a diner and skidding painfully to a halt.
Top Gear cheap car challenges sometimes involve driving to a given speed and then trying to brake within a certain range. While the obstacle at the end of the lane is sometimes daunting (e.g. a river full of crocodiles), as of Season 13 only James May has failed to stop in time, destroying his own piano as a result.
This was also the cause of Black Stig's "death" after he attempted to reach 100 mph and stop on an aircraft carrier. He mistakenly reached 109 before breaking, and plummeted into the ocean, leaving only a single black glove...
There was an episode of Smallville where Clark's powers started going haywire. When his mother calls him in for lunch, he tries to get back in the house, only to find himself at Lake Tahoe. When he tries to run back, he only makes it to Colorado Springs before his powers shut off, forcing him to take the bus home.
In an episode of Lois and Clark, Clark was able to pull this off against a nemesis who had just stolen his superpowers by taunting her. Justified in that it was the very first time she ever used her newly acquired speed.
In an episode of The Flash series, a scientist is trying to create a super-speedster, but his test subjects burn up when they accelerate, indicating that not only do they lack speed-resistant cells of the Flash, but the subjects can't slow down either, as only an idiot keeps running if they are overheating. He solves the problem by cloning the Flash.
The Flash himself had this problem in the pilot episode. He takes off at a dash, panics and puts on the brakes, and finds himself 30 miles from where he started.
Some old DOS games have this problem. Instead of timing animations and moves with a real-time clock, the game simply runs as fast as the processor will allow, which at the time meant minor variations in speed between different computers, but today a single button tap can send your character dashing across the screen. The computer-controlled enemies, of course, don't have this issue. This is why emulators like DOS Box have a throttle key.
The Elder Scrolls III: Morrowind. Scrolls of Icarian Flight allow you to jump extremely long distances, but don't grant you any protection against falling from that height (such as the Feather Fall status effect). Splat. It's actually possible to survive the landing, but it's really a matter of luck.
The use of these scrolls does allow one to sequence break through the main quest, completing it in less than fifteen minutes, rather than several days.
Abusing alchemy can lead to this trope as well. If your speed is too high, a single button press will move you until you meet a wall. That won't kill you. But if there is anything like a ramp ahead, it will get you flying, so you have to be ready for the fall.
The game also includes the Boots of Blinding Speed. While wearing them you move incredibly fast... but you also can't see anything. Apparently quite a few previous bearers of these boots ended up on the wrong side of a cliff.
Unless you are a Breton. In that case, you can still see, things are just a bit darker than they usually are.
In Super Smash Bros. Brawl, numerous characters have special moves that will cause them to quickly move forward in any of a number of ways, whether it be a Flash Step for the Star Fox trio, a flying headbutt for Luigi and Pikachu, or a motorcycle for Wario. These can easily send you off the side of the screen or the stage if you aren't careful, and in the latter case, you may not be able to get back on, due to said specials removing your ability to take any further actions until you touch the ground in the case of some characters.
Wario plays the trope even straighter if you use the bike while he's transformed into Wario-Man, as it moves about four times as fast (But causes a proportionally higher amount of damage).
Sonic in general can suffer from this, thanks to his ridiculous running speed as well the speed of both his side B and down B specials, all three of which are essential to using him effectively. Thankfully, he also has a superb recovery special to get him back on the stage in the all too likely event he accidentally runs off.
Bunny Hood wearers in general can suffer from this, especially if they're one of the faster members of the cast like Fox, Captain Falcon, or the aforementioned Sonic.
It's even more funny with the passenger mounts if one is a Paladin, Druid, Engineer, Mage, or Priest. Jump off a cliff with a passenger, dismount and bubble/slow fall/levitate/parachute cloak/flight form.
Averted in City of Heroes, where those who take the Superspeed power are able to start, stop, and turn on a dime.
EVE Online plays with this a bit. Failing to slow down while approaching another ship will usually cause a collision. No damage is taken however.
In any game where a "speed up" or "(insert character name here) moves faster" cheat is discovered and used via a Gameshark, Action Replay or some other cheat device, the result is exactly what it says on the cheat and the character moves to incredible speeds more times than not. However A) some games do this a little too well, leading to the aforementioned example above of characters crashing into walls or leap off platforms to their dooms faster than you realize what the hell you're doing, B) it is kind-of-sort-of-not-really exactly what it says on the cheat where they are faster than normal, but not enough to, say, beat Sonic in a footrace anytime soon, or C) it works well and you can still control the character in most cases, but the code caused everything else in the game to speed up just as much, making it harder than normal or just not worth using in the first place.
Road Rash 64: Insanity Mode bikes for Player 1 are awesome, right? Not so much in some Big Game modes, or in Be The Cop mode, where if you crash, you lose. Good luck feathering the throttle on bikes that were only made to go in a straight line at 500+ mph.
Video Game/Dakar 2 has an Action Replay code called "make the game fun!". It reverse-scales the gears and makes first gear into this trope. While it can be fun to launch a truck over the entire track, it will usually cause you to lose the race, because you're going to miss a checkpoint.
Subverted with the "race down the mountain" track, where the last checkpoint is lined up perfectly with the second-to-last and the finish line. You can pull off an extreme Dukes Of Hazzard moment, using one of light trucks (complete with Dixie horn!).
The 300cc and above cheat codes in Mario Kart DS are exactly like this, to the point it's pretty hard to turn, and power slides actually slow you down... You also seem to take off when you hit a ramp while using it, which is never a good way to stay away from bottomless pits. There's also the Aero Glider, which has the effects of this trope not purely due to speed, but because it's stats for handling and drift are awful, so it's like driving on ice (and hitting all the walls in the process).
Similar to the above comment about cheat devices, games with speed power-ups can result in this problem if you collect too many. The Gradius games are a prime example - in fact, later games in the series and spin-offs include a Speed Down power-up that is not a Poison Mushroom, particularly if the random power-up has thrown speed boosts at you too many times (or you foolishly activated it too many times).
In Zone races in Wipeout HD, your car gradually increases in speed (no brakes!) and continues to do so until you sustain too much damage and crash.
In Ratchet & Clank: Going Commando, you can't stop or steer at all for the first couple of seconds after you activate the Charge Boots, making it easy to fly off a cliff it there's one anywhere nearby. Latergames had you regain control sooner, but there's still a risk.
A Minecraft glitch can create this. About a minute into this video. 
In Warhammer 40,000: Space Marine your Marine Character in full Powered Armor needs a good 10 feet to stop when running at full speed. Handy when you're rushing to an enemy, not so handy when trying to round a corner.
Micro Machines series has a few stages using high speed buggies and sport cars. Considering the speed and the top-view camera, they turn some stages into That One Level since it's too late to stop and take at turn when you realize there's a corner or a pitfall up ahead.
A more traditional example is that it almost always takes several seconds for Sonic (or any of the other characters, but especially Sonic) to slow down from full speed.
A less gameplay-related example would be Metal Sonic. His main weakness is that his speed relies on the engine in his torso. While he's one of the fastest characters in the series, his lack of friction and aerodynamic nature means he crashes into things very easily.
In Pokémon Heart Gold and Soul Silver's PokéWalker, sometimes your Pokémon runs ahead of you before it notices that it went too far from your distance, and will come running back.
Due to the small planet size in Spore's Galactic Adventures expansion, it is completely possible to go fast enough to send your captain into sustained orbit with a high enough elevation and clever use of jump pads. Several player-made levels use even this as a game mechanic.
Quick Man in Mega Man 2 is so fast, even his optic sensors can't catch up to him; this flaw causes him to constantly run into walls seconds before he notices, leaving him wide open for a counterattack.
Tribes: Ascend Revolves around moving really, really fast while essentially frictionless to avoid ending up dead when grabbing the enemy's flagnote While you can get friction back to stop and turn quickly at any time, this is suicidal at best. One of the Doombringer's most powerful defensive weapons is their forcefields - not only does it absorb weapon fire, if an unfortunate or unaware enemy comes at your flag from the wrong angle, they can slam into the barrier hard enough to kill themselves.
Racing games with extremely fast vehicles can often fall into this because the vehicle moves almost too fast for the player to keep up. Good examples include Burnout and wipEout, which often unlock both the fastest class of vehicle and a new set of tracks the player is completely unfamiliar with at the same time.
Conversely, get any new player the fastest car in the game and put them on one of the earliest tracks intended for the slower classes; between the small-scale level design and the sheer speed, they'll be crashing near-constantly.
Speaking of Burnout, in the third game a more realistic example is the Preview Event type, which often put you in much faster cars than your current class on tracks you probably haven't raced on yet. The one in Europe in the Formula One car deserves special mention due to it dropping you in literally the fastest car in the game while you're still in the second-slowest class of cars.
There was one episode of Dexter's Laboratory where Dexter tried to give himself various superpowers but ended up with unintended side effects. When he gave himself super speed, he could run around the world in an instant, but when he tried to stop he ended up skidding all the way around the world again.
Someone failed physics, since friction is what generates traction to begin with. Frictionless shoes would make it impossible for him to travel, he would either run in place or slip and fall with the first step.
This is Hand Waved by Jimmy saying that the shoes were propulsive, and frictionless, which only makes sense on paper.
Since when does Jimmy Neutron ever go anywhere close to real physics?
Happens to Bumblebee in Transformers Animated when he gets a massive speed upgrade; fortunately, Optimus Prime is able to save him from driving off a cliff, but it ends up being his fault that the villain gets away.
Parodied in the Futurama episode "How Hermes Requisitioned His Groove Back", as a bureaucrat on an ultra-slow scooter can't stop from rolling into a stack of boxes and jostling them slightly.
There's an episode of Teen Titans in which Kid Flash is running away from Madam Rouge and ends up smashing into a brick wall at top speed. He acts dizzy and out of it for a few seconds until she catches up to him.
In the finale of the Project Cadmus arc of Justice League Unlimited, The Flash has to run so fast to defeat the Luthor/Braniac merger that he warps out of reality for a moment. When Hawkgirl pulls him back, he comments that if he ever runs so fast again, he may disappear for good.
In the first season of Justice League, The Flash was held back a lot by being tripped or clotheslined by objects that he had no excuse for not seeing coming or reacting to.
In the cartoon of Young Justice, Kid Flash has this problem, running into a metal door because he didn't have enough space to stop. Though this might just have been because he was in a hallway.
The Discworld's Puzuma example was probably based on the old urban legend (False, but still funny) about a car mounted with JATO-rockets embedded in a cliff-face somewhere in Arizona.
This is the cause of many car accidents, not to mention the yellow / amber lights on traffic signals: it's a warning that you will be required to be out of the intersection soon. If you are going too fast to stop, it is acceptable (indeed, preferable!) that you keep going, instead of trying to stop and merely blocking up traffic.
On some kinds of ice, five miles an hour can be too fast to stop. Definitely Truth in Television.
Trains are very heavy, can go very fast, and their particular method of locomotion results in little friction. The end result is that they can take a mile or more to stop.
This is even worse for very large ships. While they move relatively slowly, it takes them hours to get rid of all the momentum, because of their ludicrous mass and the fact that water is much worse at slowing someone down than the ground. A big freighter hitting a pier at only a few knots can crush in the bow by twenty feet.
Anyone who has learned to skateboard has encountered this problem.
As does anyone on a bike coasting downhill fast enough that the choices are 1) hope you miss the trees (or car) at the bottom, 2) slowly (but in a way that damages the brakepads) apply the brakes a little at a time as they grind but don't quite grab, or 3) hit the brakes fully or flip to one side, and don't quite stay in the sweet spot of possibility 2.
Thanks to Newton's Laws, this can even be a problem when running unassisted. While you're unlikely to go flying off a ledge, it does take a few feet for the body to "backpedal" enough to come to a stop. Everyone has run into at least one wall because they stopped or turned too late.
Something a lot of sports teach players is avoiding this trope. It's usually much better to be fast and maneuverable than too fast and stopping to turn.
Has happened a few times with Mythbusters experiments. Such as the "Instant Convertible".
This is a major issue with heavier than air aircraft; as air friction is sharply limited, a quick stop with such craft while travelling at high speeds is impossible. Worse still are airplanes; if they lack vertical takeoff and landing capabilities (as most do), they literally CANNOT stop while in the air; if they were to try, they would start falling, resulting in velocity in a different direction.
Spacecraft have it even worse in some respects, as "relative to what" becomes a major issue. Spacecraft speeds are often extremely high relative to other objects and as such have a difficult time braking, especially given that the only thing they can use is their own thrusters - space is essentially a vacuum, and entering an atmosphere at orbital speeds is suicidal.