0 mph to 60 mph in 2 seconds, what's the acceleration? (the answer is NOT 30)

[@bprpmathbasics]

Tricky question 4:53

[@suryanshbiswas]

With constant acceleration? or not.

[@TenQYT]

120mph

[@torarne7796]

Assuming constant acceleration (which it won't be with a real Tesla), slightly less than 120 mph if you take relativity into account.

[@CasiMediocre]

It's easy! (60 mph, 120 mph] 😂

[@TenQYT]

@@torarne7796 Wow! In-depth. I think he meant just constant acceleration. Also, the "Tricky Question" had no Tesla mentioned.

[@Hdtjdjbszh]

it hurt my european hart to see you do all that work and then not use SI units

[@z4zuse]

Not just European, practically the rest of the world

[@MarieAnne.]

It hurt my Canadian heart to see heart spelled h-a-r-t. But hey, that's life.

[@xinpingdonohoe3978]

​@@MarieAnne. It hurts my British heart to see a Canadian.

[@jensraab2902]

@@MarieAnne. Oh deer, here we go again.

[@christopherneil8265]

You know most sciences use metric in the US right? It hurt me too

[@Jackibelle]

Miles per hour per second is a very good unit for describing acceleration of cars whose speed is normally reported in miles per hour.

[@vytah]

There's a video from Joseph Newton about cursed units and the final example he gives is 10^(-10) cmSTP³·cm/cm²·s·cmHg and all those four instances of centimetres mean something and make sense.

[@timsloane]

I agree, but I suspect it's because I'm an engineer. The specification a car has is the time in seconds to reach a speed measured in mph, so 30 labeled with the proper units is the most natural answer, and I think the best answer. However, I would format the units as mi/hr⋅s. Using two slashes in your units is a really bad practice.

[@mike140298]

​@@timsloane at the same time, when you're communicating to the general public instead of engineers, a second slash might be better.

[@bjornfeuerbacher5514]

@@timsloane I'd use mi/(hr⋅s). Otherwise it looks like as if one first divides the mi by the hr and then afterwards multiplies the result with the s.

[@Micboss1000]

I thought you were going to show that we completely misunderstand how acceleration works, but it's just nitpicking about units and notation.

[@bprpmathbasics]

If you meant how people commonly assume all accelerations are constants, then that’s what my question at 4:54 is for.

[@timward2001]

Actually, when you're talking about car performance "miles per hour per second" is a perfectly reasonable unit to use (for non-SI people). So I'll stick with the original answer of 30. Until you bring in physics of course. If what the car drive chain can actually supply is a certain amount of *energy* per second then the acceleration isn't going to be uniform, is it ...

[@pietergeerkens6324]

Precisely. 30 mph/s is readily understood by anyone in the U.S., and anyone over 50 in UK or Canada. 44 ft/s/s is only understood by physics majors, a much smaller number of people.

[@timward2001]

@@pietergeerkens6324 Well, I knew that 60mph = 88fps, I'm pretty sure I was taught that in primary school, it was just like learning that £1 = 240d, just part of the system of units we had then.

[@pietergeerkens6324]

@@timward2001 Yep. I learned that in Grade 11 physics also, in 1972, though I don't use it much anymore.

[@Insightfill]

And THIS is how you crash a probe into Mars.

[@infrences]

Clever reference

[@erwinmulder1338]

Wrong! The real answer should obviously be given in furlong per fortnight squared.

[@richardhole8429]

Furlongs per fortnight, my very favorite unit of Velocity, thanks!

[@ad-mc]

You need to factor in leap years in your fortnight begins in late February

[@unholycrusader69]

Screw the CGS/SI/Imperial systems! All hail the mighty FFF system!

[@mike140298]

Nah, I just want megaparsec per light fortnight per plank second.

[@marilynman]

The last time someone used that unit that person went to the psychiatric. Don't do it.

[@lukchem]

You could also just convert the 2 seconds to hours and then divide. Then you would get mph^2 which is also a valid way to express acceleration.

[@toast_recon]

30 mph/s is the best answer. It doesn't play nicely with calculus or conversions, but that's caused by the problem statement, not the approach to the solution.

[@getvictored1737]

30 mph/s boom. easy.

[@BigDBrian]

it may not be 30, but it is 30mph/s :)

[@phoenixarian8513]

The acceleration written in mph/s or kph/s is ok especially in measurements of rail vehicles. That's the unit for Shinkansen. 3.6 kph/s equals 1 meter/second square or approx 0.1g. However this is a civilian unit not a physics unit. In physics we use meters/second square for acceleration and meters/second for speed.

[@wisteria4360]

For my metric brain: 60 mph = 96.5606 kmph 44 ft.s^(-2) = 13.4112 m.s^(-2) vf = vi + aΔt v = 96.5606/(60² ÷ 10³) + 2(13.4112) v = 53.64478888889 m.s^(-1) Converting m.s^(-1) to miles per hour: = 53.645 × 2.237 = 120 miles per hour Therefore: 120 mph

[@wisteria4360]

Damn makes sense kinda. It's just double. Might be wrong though

[@Elesario]

To be fair in the real world the car is accelerating against various frictions, air likely being one of the major ones (drag), so the acceleration will taper sharply as the resistance against it gets higher and higher. Just looked up that air resistance is calculated with: F = 1 / 2 ∗ p ∗ v ^2 ∗ C ∗ A (removed the subscripts) , but don't ask me to figure out the answer adjusted with this 😂

[@ilburrito0059]

​@@Elesario yeah but this is a basic physics problem so we assume that there are no frictional forces

[@jensraab2902]

And this is why one should also use units. It drives me crazy that so many folks who present math problems simply omit units and then add them back in the result. Be better.

[@torarne7796]

@@jensraab2902 It's likely the same people who fly their jets out of fuel. en.m.wikipedia.org/wiki/Gimli_Glider

[@jensraab2902]

@@torarne7796 Ah, I wasn't aware of that one (only of the loss of the Mars Climate Orbiter). Obviously, I don't want anybody to be hurt but I can help having a little bit of schadenfreude whenever the insistence of Americans on their joke units causes issues. (No schadenfreude about the loss of the Orbiter because this truly is a loss for all of humanity, not just NASA.)

[@torarne7796]

@@jensraab2902 If I recall correctly, the accident was right after Canada switched from imperial to metric. But more important than which units to use, is using units at all.

[@lamaistul]

Just use the metric system FFS... 😆

[@JimmyMatis-h9y]

Just don't eat meat ffs See? Equally arbitrary.

[@stupidteous]

@@JimmyMatis-h9y not really... not at all actually

[@pousarmic8155]

Bro, definition of a meter is "the distance the light travels in vacuum for 1/299,792,458 seconds". The definition of a mile is governed by the meter. Therefore, mile is so made up shit. Use SI system. Its more natural ig.

[@ReZeroCultLeader7594]

metric system is evil

[@nanamacapagal8342]

​@@pousarmic8155 And who decided one meter being exactly that oddly specific fraction of the speed of light makes it any more objective? Just use the raw constants of the universe. Can't get more objective than that

[@57thorns]

In this case, talking about acceleration for cars, that is exactly how it is done. How fast is the car going after one second if the accelration is constant? You can _immediately_ spot that the speed is 30 furlongs per week, miles per hour, AU per year or whichever speed unit you are using, if you go from 0 to 60 in two seconds.

[@57thorns]

In a vacuum, and a lossless drive train, the car will go 120 mph after four seconds.

[@KenseiShiro]

i see so the answer is 30

[@Kyrelel]

Nope. Have another think about it.

[@zachansen8293]

now can we compute the distance traveled during that 2 seconds?

[@Kyrelel]

132ft

[@zachansen8293]

@@Kyrelel show your work or no points :) But this is actually a really simple "integration" -- such that it's just the area of a triangle, huh?

[@joshuahillerup4290]

This made me so happy I did this sort of question in Canada and not the US

[@MeAlek]

108'000 mph/h In standard units: 13.4 m/s² (standard: 'm' is meter) After 2 more s, speed is 120 mph

[@blankspace178]

If a vehicle accelerates from 0 to 60 mph in 2 seconds, its acceleration is approximately 10800 miles per hour per hour (or 48.89 meters per second squared). Explanation: To calculate acceleration, we use the formula: acceleration = (final velocity - initial velocity) / time. In this case, the initial velocity is 0 mph, the final velocity is 60 mph, and the time is 2 seconds. Plugging these values into the formula gives: acceleration = (60 mph - 0 mph) / 2 seconds = 30 mph/second. To convert this to miles per hour per hour, multiply by 3600 seconds per hour, resulting in 10800 miles per hour per hour

[@danaldrich2171]

Could take it one step further. 1g is 32 f/s^2. So the acceleration is 1.375G.

[@Brid727]

well, i assume that it's starting from rest and seeing the question, i think it's safe to assume that u=0 m/s the tricky part is v, where v=60 mph so, v=(60*1.61*1000)/(3600) m/s = 26.82 m/s t=2 sec so, acceleration, a=(26.82 - 0)/2 = 13.41 m/s^2 yes i use the si units but that's how id solve it for the bonus question, i have to assume that the car moves at uniform acceleration or else that would be unsolvable for me as above, a=13.5 m/s^2 time, t=2 sec initial velocity, u=60 mph = 26.82 m/s(as above) well, i would use the v^2 = u^2 + 2as formula, but i don't have the value for s so we're gonna use V = u + (1/2)at [formula for uniform velocity] applying the values, V = 26.82 + (1/2)*13.41*2 = 40.23 m/s now, we also know that, V = (u+v)/2 so, u+v = 2V v = 2V - u substituing the values v = 2*40.23 - 26.82 = 80.46 - 26.82 = 53.64 m/s bruh i just realized my answer must be in mph oh well, v = (53.64*3600)/(1.61*1000) = 119.94 mph

[@krabkrabkrab]

Nice to see you doing physics. You do it the same way I emphasize with my students. But I actually add a step to explain the units conversion. I say: 1hr=3600sec is a true equation. divide one side by the other and you get 3600sec/hr=1. And you can always multiply an expression by 1 without changing it.

[@YoVariable]

Finding acceleration the metric way: Convert 60 mph to m/s: 60 mph * 1609 m/1 mi * 1 hr/3600 s ≈ 26.82 m/s Use the kinematic equation Vf = V0 + at to solve for a 26.82 m/s = 0 m/s + a(2 s) 26.82 m/s = a(2 s) a ≈ 13.41 m/s^2 In imperial units: a = 13.41 m/s^2 * 3.28 ft/1 m a = 44.00 ft/s^2 -------------------------------------------------- Finding the speed in 4 seconds: Vf = 0 m/s + (13.41 m/s^2)(4 s) Vf = (13.41 m/s^2)(4 s) Vf ≈ 53.63 m/s In imperial units: 53.63 m/s * 3600 s/1 hr * 1 mi/1609 m = 120.0 mph Vf = 120.0 mph

[@greenpenguin3154]

This is why we use ms^-1 or kmh^-1 outside of America

[@kmsbean]

wouldn't it be easier to just to it in kph (100km ~ 60 miles, technically 95.56) to get 14m/s^2 (13.41 m/s/s if you want to be precise)

[@Risu0chan]

If you're an American driver, 30 mph/s makes sense. If you're a physicist, then it's 13.4 m/s² or 1.37 g.

[@Michael43713]

You say the answer is not 30 yet you do not state the dimensions.30 miles/hr/s is correct. It means your speed will increase by 30 mph for every second you travel. Then you go on about the number of feet in a mile.

[@richryugaming6911]

Hi Bprp, I’ve been a fan of your videos, and your main channel has taught me calculus better than anyone else. I have a question about this problem. There is a formula in physics that uses : a = acceleration Vf = Final velocity Vo = initial velocity t = time And this is the formula, Vf = Vo + at So I was wondering on what if we use this formula. Edit : My solution to your question in the end. Vo = 0ft/s t = 4s a = 44ft/s Vf = ? Vf = 0 + 44(4) Vf = 44(4) Vf = 176 ft/s Please correct me if I’m wrong

[@koenth2359]

I'm a physics teacher, maybe I can help you out. I think you're mixing up two formulas here. For constant acceleration a, we have the following formulas for speed v(t) and position x(t): v(t) = v(0) + at x(t) = x(0) + v(0)t + ½at² So for the final velocity you need to use the first of these.

[@richryugaming6911]

@koenth2359 Yes, thanks. It’s been long since I’ve done kinematics. I’ve been doing electromagnetism instead so I’ve been getting a bit rusty.

[@Asiago9]

I found the acceleration in a different way, actually in mi/hr², or 108,000 by multiplying 60mi/hr by 3600s/1hr by 1/2s

[@tonya1cocov237]

The final velocity is going to be 176 ft/s

[@michalw6965]

You could have changed mph to m/s and then solve equation with real life units ;)

[@jamesMarjan]

Great way to start the day.

[@Anti_During]

if 60 is km/h , than a=8.3 m/s^2

[@RAG981]

30 mph = 44 fps. I learned my applied math in the 60's. acc = 88/2 = 44 fps^2. And v = u + at. Shocking video I'm afraid.

[@Doraemon-jm5oo]

After applying v = u + at formula, I am getting 120 mph.

[@ichanmich]

question is, why you calculate a velocity when the acceleration is asked for...

[@PigeonSwag]

i dont get the question at the end, are we assuming a constant acceleration? or is it that as the target speed is 60mph (or 88ft/s, which should really be 26m/s tbh) there will be no further acceleration? imo theres not enough information given

[@-wx-78-]

30 miles per hour-second seems fine to me: it says exactly how much mph that vehicle gains each _second_. Remember kilowatt-hour (or mythical man-month). 😉

[@ichanmich]

our new TV gives its energy consumption as "kWh / 1000 h"

[@tinyeung3468]

v = u + at 88 fts^-1 = 0 + a * 2s a = 44 fts^-2

[@JJ_TheGreat]

2:35 Use dimensional analysis!!!!

[@Iomhar]

Let us know when you make a 21st century version of this video.

[@Артём-к6и6м]

How much is it is squared football fields?

[@johanndohmann1281]

a car accelerates from 0 to 80 mph within half a minute. the mass of the car is about 3000 pound. calculate the kinetic energy and convert the value to gallons of fuel or, if prefered, to BTU. best wishes from the metric world😂😂😂😂❤❤

[@timward2001]

If you fly you find yourself doing those sorts of calculations, including multiple unit conversions, for each flight.

[@johanndohmann1281]

@timward2001 yes, i agree. long time ago i worked in a lab close to toronto. i had missed my calculator and my conversion table. yes, conversions like those are real and confusion as well. have a nice day.

[@alipourzand6499]

1.47g, unity system independent! ☺

[@LordQuixote]

The problem is that in math classes the units aren't treated like the constants that they are

[@elliuozaG]

I was gonna say the the unit is miles per hour per second but after watching it whole, I throw the towel. You turned a simple answer into a foot in my mouth.

[@asdfqwerty14587]

There isn't really anything technically wrong with that, it's just a matter of conventions. In some contexts that unit might make sense. I mean, in this context, miles per hour per second.. probably does make the most sense to be honest (assuming we aren't talking about whether we should convert miles to km or not which is a completely different debate). When you're talking about the speed of a car you're pretty much always talking about the speed in miles per hour (or km per hour), but when you're talking about the acceleration nobody cares about the acceleration the car does in an hour, so showing the rate that the speed in mph changes per second is actually probably the most useful metric if you were working with a real world problem. Of course, that's just specific to this particular context - there are tons of times when it is appropriate to switch the units to something else.

[@57thorns]

For an impact like that, the preferred unit is g (as in earth's average surface gravity 9.81 m/s^2). The car goes from 0 to 96 km/h in two seconds. 96 km/h is approximately 27 m/s (the only hard part here is the 3.6 factor konverting km/h to m/s). So 13 m/s^2 or 1.3g which was surprisingly little. Two seconds is a long time. 🙂

[@nvapisces7011]

108000 mi /h²

[@ichanmich]

no, it's not "'30". Because "30" is a unit-less number and not an acceleration.

[@bokkenka]

Alright... I am a self-admitted pedant, but this one gets a tumbs-down-frowny-face-fart-noise from me. If the problem is given in mph, then the answer should be too. "80640 furlongs per fortnight" is *technically* correct, but is wrong. If you are given the acceleration of 60 mph in 2 seconds, you do not have enough information to calculate the actual curve, so the only justifiable answer to the end question is "not more than 120 mph" because we know that acceleration of a car is not linear but we do not know by how much.

[@bloviatingbeluga8553]

now do it with kph! 😮

[@Hdtjdjbszh]

answer the end question will be 53 and a bit

[@ActualDumBatcha]

BEFORE WATCHING: in first second it goes x mi/h/h. it goes x^2 mi/h/h. x^2 + x = 60. x^2 + x - 60 = 0. therefore x = (-1 +sqrt[241])/2 (no minus because it's accelarating) ~ 7.26mi/h/h.

[@MarieAnne.]

First, that's the average over the first second (assuming your model of x and x^2 over the first 2 seconds is correct). Second, since both x and x^2 are the average acceleration over 1 second intervals, their units should be in mi/h/s. To find the average acceleration over 2 seconds, we get: [(1s * 7.26mi/h/s) + (1s * 7.26^2mi/h/s)] / (2s) = 29.9838 mi/h/s which pretty much matches just dividing change in speed by total time (difference is due to rounding of x)

[@zinc_magnesium]

@@MarieAnne. Good correction. I would also add that “assuming the model is correct” would be a little bit silly. Why would the car be accelerating 7.26 mi/h/s for one second and ~52.71 mi/h/s in the next? Did the car decrease in mass by a factor of 7.26 instantaneously at the end of the first second? Or did someone hit the gas pedal in such a way that they exactly squared their acceleration? Even if you say that the force that accelerates the car might not be the limiting factor, and that it is actually the power provided by the chain drive which determines the behavior, you would expect to see acceleration decrease over time, not increase wildly in the space of a second.

[@ichanmich]

you ought not double-divide without parenthesis.

[@George0rw377]

i miss my SI units. *sigh*

[@Dotandman2]

120mph

[@robertpearce8394]

Use metric

[@rltt379]

just write 30mps/s it's not hard to visualize for americans I'd imagine and considering neither units are supposed to be used for physics who cares

[@marcd.1166]

math in imperials ... forget about it!

[@jonathanwilson7032]

ft/s … so cute 😂

[@kdog3908]

**scowls in metric**

[@vytah]

In metric, you'd have the same discussion: is 50 km/h/s better, or is 13.9 m/s² better?

[@kdog3908]

@@vytah The scowl isn't about the discussion. **scowls metrically more**

[@TexasEngineer]

The answer to your last question is unanswerable. The acceleration from 60 to 120 mph will take longer than 2 sec because of wind and rolling resistance. Wind resistance is a power function and non-linear and must be measured and not extrapolated. Even rocket ships in space experience a different type of change because they loose mass as they accelerate.

[@MitchBurns]

Why not just say 30 miles per minute squared. The math works out since there is a common conversion factor of 60.

[@Golgo1412]

Ever seen that use in real life?

[@MarieAnne.]

@@Golgo1412 No, but it's not wrong. If question gives mixed units without specifying what units to use for answer, then I don't see why miles/min^2 should be any less valid than ft/sec^2.

[@joaojosevaldo]

the kind of problem you don’t have when you are not american lol

[@sh1sh1maru]

I'm not religious, but for God's sake, use meters, not feet!

[@richardhole8429]

God created our feet. Lighten up!

[@LoneCat2137]

3:16 ew

[@hehehehaw6969]

Interesting

[@reelkanha]

The hell is a feet or a mile. 🦅system is dumb

[@teelo12000]

30mphps

[@ichanmich]

oh, the humanity!

[@EyeSooGuy]

Tesla? Ugh. Damn repubs.

[@Icematt12]

For the ending, im assuming with a Tesla acceleration is not constant over 4 seconds. So

[@TheKnowledgeOfScience]

😢

[@minecraftgamer4290]

120mph another two seconds

[@Hdtjdjbszh]

oh sorry, that's not it.

[@pierrefraisse8610]

You are supposed to be smart, pls use Km/h!.

[@MarieAnne.]

Technically the SI units for velocity and acceleration are m/s and m/s^2 respectively.

[@major__kong]

There's is nothing smart about the metric system. When I was learning it in school in the US early 1980s, the "nice" feature was that it uses powers of 10. However, in practice, that doesn't matter. Numbers aren't any "nicer" in the metric system compared to imperial. As a practicing scientist and engineer for over 30 years now, I don't see a compelling reason to use any system over another. The more important thing is a standard whatever the standard is. I do want to point out that my house, built in 1963 in Ohio, was built to metric standards. The studs in the walls are exactly 40.64 cm on center. Regardless of the system, there are compelling practical reasons to use other bases such as base 12. In English and German, the numbers 1-12 don't use a naming convention. That doesn't happen until you get to 13. Now ask yourself why? Hint, it has to do with the numbers of factors of 12 compared to 10 and how people lived hundreds of years ago. Finally, if someone brings up the Mars thing, that was an example of poor systems engineering practices and lack of testing not a units problem. That was the proximate / superficial cause

[@pierrefraisse8610]

@@major__kong 12, number of phalanges of a hand.

[@ichanmich]

K : Kelvin k : kilo

[@pettriksteig6186]

use metric units ! no wonder, you vote for trump

[@Hieltiik]

use please metric system

[@aidapex71]

5 minutes ago

[@beaudavis3808]

It's average acceleration is 44 ft/sec^2

[@RylanceStreet]

Or about 1.37 g.

[@Watashi-Wa-Kat-Desu]

Who uses feet? Use m/s^2

[@AndreChaosweapon]

@@Watashi-Wa-Kat-Desu any who use imperial metrics they have to use miles per hour and feet per second...

[@Watashi-Wa-Kat-Desu]

@@AndreChaosweapon ah but why? m/s^2 is the SI unit