# On Acceleration: A Math Question And A Physics Question **URL:** \ **Category:** Factual Questions\ **Created:** [November 27, 2020, 2:14pm UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592 "2020-11-27T14:14:44Z")\ **Posts on this page:** 16\ **Page:** 1
**Author:** ![HeyHomie](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/heyhomie/32/207_2.png) [@HeyHomie](https://boards.straightdope.com/u/HeyHomie)\ **Post date:** [November 27, 2020, 2:14pm UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/1 "2020-11-27T14:14:44Z")
Math: A vehicle accelerates at 10km per hour per second. So in ten seconds, its speed has gone from zero to 100km/hr; in 20, it’s up to 200km/hr; etc. What is the formula to determine how far the vehicle has moved after _n_ seconds? Physics (or maybe Medicine): for a passenger in that vehicle, how long could he or she endure that acceleration before experiencing any negative effects? More or less infinitely? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 27, 2020, 2:36pm UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/2 "2020-11-27T14:36:13Z")
Accelerations in mixed units are very difficult to work with. So let’s start by converting that to m/s^2. 3.6 km/hr = 1 m/s, so 10 km/hr/s is 2.78 m/s^2. The total distance traveled is given by x = v\_i_t + 1/2 a_t^2. It sounds here like we have an initial velocity of 0. So that reduces to x = 1/2 a\*t^2. For your last question, the total acceleration experienced by the passenger would be the Pythagorean sum of gravity and the vehicle’s acceleration (Pythagorean because they’re at right angles to each other). g = 9.81 m/s^2, so the total acceleration would be 10.12 m/s^2, or about 4% greater than normal gravity. I’m not a physician, but I can’t imagine there would be any significant medical effects at all from a gravity 4% larger than normal. This is assuming that this is a vehicle moving horizontally on the surface of the Earth. If you’re thinking of a rocket, then there probably wouldn’t be any gravitational component, and the total acceleration experienced by the passengers would be just the acceleration of the vehicle. In this case, any problems that would arise would be from the acceleration being too small, not too large. But we know basically nothing about the long-term effects of low but nonzero acceleration on the human body (the most extensive experiment that’s been done is the few days the Apollo astronauts spent on the Moon). ---
**Author:** ![Quercus](https://avatars.discourse-cdn.com/v4/letter/q/7ab992/32.png) [@Quercus](https://boards.straightdope.com/u/Quercus)\ **Post date:** [November 27, 2020, 2:51pm UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/3 "2020-11-27T14:51:22Z")
> [@Chronos](#): > > If you’re thinking of a rocket, then there probably wouldn’t be any gravitational component, and the total acceleration experienced by the passengers would be just the acceleration of the vehicle. To clarify, what I’m sure Chronos meant, this is for a rocket in outer space. A passenger in a rocket blasting off straight up from the surface of the Earth would experience gravity plus the acceleration. Which is only about 1 1/4 of regular gravity, so pretty bearable. ---
**Author:** ![FrenchDunadan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/frenchdunadan/32/5449_2.png) [@FrenchDunadan](https://boards.straightdope.com/u/FrenchDunadan)\ **Post date:** [November 27, 2020, 4:27pm UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/4 "2020-11-27T16:27:55Z")
For a rocket aiming to space, acceleration is far more important than 2,78 m/s². cite : [File:Apollo 8 acceleration.png - Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Apollo_8_acceleration.png) For the endurance of the crew, less than 1 g (=9,81 m/s²) is sustainable during a great time for a trained pilot. 3 g or more will cause loss of consciousnesses or even injury in the neck or organs in a few minutes or even seconds. cite: [Acceleration stress | physiology | Britannica](https://www.britannica.com/science/acceleration-stress) ---
**Author:** ![mixdenny](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mixdenny/32/2962_2.png) [@mixdenny](https://boards.straightdope.com/u/mixdenny)\ **Post date:** [November 27, 2020, 5:46pm UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/5 "2020-11-27T17:46:14Z")
From a US car guy’s perspective. The car has a 0 to 60 MPH time of just under 10 seconds. That’s not neck snapping but it is probably about as fast as my Scion accelerates. I don’t think that would be comfortable for a long period. Neck strain would be an issue. ---
**Author:** ![am77494](https://avatars.discourse-cdn.com/v4/letter/a/d2c977/32.png) [@am77494](https://boards.straightdope.com/u/am77494)\ **Post date:** [November 27, 2020, 5:53pm UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/6 "2020-11-27T17:53:41Z")
> [@HeyHomie](#): > > Math: A vehicle accelerates at 10km per hour per second. So in ten seconds, its speed has gone from zero to 100km/hr; in 20, it’s up to 200km/hr; etc. In the world of math and physics, this is a great problem to solve. However, in the real world, car acceleration is not constant. This is because the engine has different horsepower and torque at different speeds. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [November 27, 2020, 5:57pm UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/7 "2020-11-27T17:57:23Z")
It probably would be comfortable if the neck was supported correctly. After all, lying on your back in 1 gee is pretty comfortable, unless your head is hanging out past the end of the bed, in which case there is neck strain. ---
**Author:** ![mixdenny](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mixdenny/32/2962_2.png) [@mixdenny](https://boards.straightdope.com/u/mixdenny)\ **Post date:** [November 27, 2020, 11:46pm UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/8 "2020-11-27T23:46:34Z")
Exactly. Driver’s head rests are usually too far back to be comfortable. Back seat passengers could slouch down a bit to utilize the rest. Right after I posted earlier I tried hanging my head over the bed. I didn’t last 30 seconds. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [November 28, 2020, 12:05am UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/9 "2020-11-28T00:05:28Z")
Yeah. I don’t even want to try it. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [November 28, 2020, 6:28am UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/10 "2020-11-28T06:28:15Z")
> [@FrenchDunadan](#): > > 3 g or more will cause loss of consciousnesses or even injury in the neck or organs in a few minutes or even seconds. 3 g? No way. Any reasonably healthy adult can sustain 3 g for hours in a reclined position. Trying to stand would be a different story, of course. The Gravitron ride at various amusement parks hits 3 gees for at least a minute. Just about anyone can ride one without injury. I was able to get on my knees and crawl around the inside without too much problem (requires a compliant operator…). ---
**Author:** ![FrenchDunadan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/frenchdunadan/32/5449_2.png) [@FrenchDunadan](https://boards.straightdope.com/u/FrenchDunadan)\ **Post date:** [November 28, 2020, 7:25am UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/11 "2020-11-28T07:25:38Z")
Well, the important words are here “in a reclined position”… If the acceleration is towards the feet, humans can sustain up to 7 g before experiencing blackout (not enough blood in brain), but if acceleration is toward the head, 3 g is enough to cause red veil(don’t know if the exact English term) caused by too much blood in the brain. With an acceleration tangential to trajectory, things may vary, but generally it’s the head that deport to the side… so neck injury probable. I have several sources, but in French… ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 28, 2020, 1:31pm UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/12 "2020-11-28T13:31:32Z")
Heck, even 1 g will cause problems if it’s directed towards the head. Hanging upside down for an extended time is awfully uncomfortable. But I think it’s safe to assume that the passengers in our vehicle are in a reasonably comfortable pose. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [November 29, 2020, 3:36am UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/13 "2020-11-29T03:36:51Z")
> [@FrenchDunadan](#): > > red veil(don’t know if the exact English term) Redout. I.e., “red out”. In contrast, greyout is the intermediate step from lack of blood, happening before blackout. Usually, peripheral vision is lost/reduced, and the whole visual field gets dim. And yeah, I assumed–based on the OP–that the person is in a reasonably comfortable pose. Flat on the back (and perpendicular to the acceleration vector) would be best, but any reclined position is ok for moderate g-forces. ---
**Author:** ![FrenchDunadan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/frenchdunadan/32/5449_2.png) [@FrenchDunadan](https://boards.straightdope.com/u/FrenchDunadan)\ **Post date:** [November 29, 2020, 11:10am UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/14 "2020-11-29T11:10:17Z")
Thanks, I did think of redout (as analogy with blackout) but was not sure, so translated ‘voile rouge’…As for the OP, an acceleration of 1/4g is nowhere near any danger area for a passenger in a seat ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [November 30, 2020, 12:09pm UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/15 "2020-11-30T12:09:03Z")
> [@mixdenny](#): > > From a US car guy’s perspective. The car has a 0 to 60 MPH time of just under 10 seconds. That’s not neck snapping but it is probably about as fast as my Scion accelerates. I don’t think that would be comfortable for a long period. Neck strain would be an issue. For perspective, 0-60 in 10 seconds is about 0.27g, oriented front-to-rear. This is only a little more than what commercial airliners achieve while accelerating during takeoff roll. > [@am77494](#): > > In the world of math and physics, this is a great problem to solve. However, in the real world, car acceleration is not constant. This is because the engine has different horsepower and torque at different speeds. OP was pretty careful to use the nonspecific term “vehicle.” This would include wheel-driven surface vehicles with reciprocating engines and multi-ratio transmissions, which behave as you describe - but it would also include vehicles powered by reaction engines, like rockets and aircraft, which can have very stable acceleration rates within the speed ranges described… ---
**Author:** ![am77494](https://avatars.discourse-cdn.com/v4/letter/a/d2c977/32.png) [@am77494](https://boards.straightdope.com/u/am77494)\ **Post date:** [November 30, 2020, 3:15pm UTC](https://boards.straightdope.com/t/on-acceleration-a-math-question-and-a-physics-question/926592/16 "2020-11-30T15:15:41Z")
> [@Machine\_Elf](#): > > - but it would also include vehicles powered by reaction engines, like rockets and aircraft, which can have very stable acceleration rates within the speed ranges described… I am in agreement in general with your post. However, In the spirit of nitpicking, since the OP is describing startup (liftoff) from 0 speed, acceleration even in rockets is not linear during liftoff time. See page 3 and 4 here : [https://www.nasa.gov/pdf/522589main\_AP\_ST\_Phys\_ShuttleLaunch.pdf](https://www.nasa.gov/pdf/522589main_AP_ST_Phys_ShuttleLaunch.pdf)