Instantaneous speed and velocity | One-dimensional motion | Physics | Khan Academy


– [Instructor] Pretend
you are a physics student. You are just getting out of class. You were walking home when you remembered that there was a Galaxy
Wars marathon on tonight, so you’d do what every
physics student would do: run. You’re pretty motivated to get home, so say you start running
at six meters per second. Maybe it’s been a while
since the last time you ran, so you have to slow down a little bit to two meters per second. When you get a little
closer to home, you say: “No, Captain Antares wouldn’t give up “and I’m not giving up
either”, and you start running at eight meters per second
and you make it home just in time for the opening music. These numbers are values
of the instantaneous speed. The instantaneous speed
is the speed of an object at a particular moment in time. And if you include the
direction with that speed, you get the instantaneous velocity. In other words, eight meters
per second to the right was the instantaneously
velocity of this person at that particular moment in time. Note that this is different
from the average velocity. If your home was 1,000
meters away from school and it took you a total of
200 seconds to get there, your average velocity would
be five meters per second, which doesn’t necessarily equal
the instantaneous velocities at particular points on your trip. In other words, let’s
say you jogged 60 meters in a time of 15 seconds. During this time you were
speeding up and slowing down and changing your speed at every moment. Regardless of the speeding
up or slowing down that took place during this path, your average velocity’s
still just gonna be four meters per second to the right; or, if you like, positive
four meters per second. Say you wanted to know
the instantaneous velocity at a particular point in
time during this trip. In that case, you’d wanna
find a smaller displacement over a shorter time interval that’s centered at that
point where you’re trying to find the instantaneous velocity. This would give you a better value for the instantaneous velocity but
it still wouldn’t be perfect. In order to better zero-in on
the instantaneous velocity, we could choose an even
smaller displacement over that even shorter time interval. But we’re gonna run into a problem here because if you wanna find a perfect value for the instantaneous velocity, you’d have to take an
infinitesimally-small displacement divided by an infinitesimally-small
time interval. But that’s basically zero divided by zero, and for a long time no one
could make any sense of this. In fact, since defining motion
at a particular point in time seemed impossible, it made
some ancient Greeks question whether motion had any meaning at all. They wondered whether
motion was just an illusion. Eventually, Sir Isaac Newton developed a whole new way to do math that lets you figure out answers to
these types of questions. Today we call the math that
Newton invented calculus. So if you were to ask a physicist: “What’s the formula for the
instantaneous velocity?”, he or she would probably give you a formula that involves calculus. But, in case some of you
haven’t taken calculus yet, I’m gonna show you a few ways to find the instantaneous velocity
that don’t require the use of calculus. The first way is so simple
that it’s kind of obvious. If you’re lucky enough to have a case where the velocity of an
object doesn’t change, then the formula for average
velocity is just gonna give you the same number as the
instantaneous velocity at any point in time. If your velocity is changing, one way you can find the
instantaneous velocity is by looking at the motion
on an x-versus-t graph. The slope at any particular point on this position-versus-time graph is gonna equal the instantaneous velocity at that point in time because the slope is gonna give
the instantaneous rate at which x is changing
with respect to time. A third way to find the
instantaneous velocity is for another special case where
the acceleration is constant. If the acceleration is constant, you can use the Kinematic Formulas to find the instantaneous
velocity, v, at any time, t. (electronic music)

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100 thoughts on “Instantaneous speed and velocity | One-dimensional motion | Physics | Khan Academy”

  1. MadelMac says:

    Ahhh this is so good! Have been scratching my head at my textbook for 10 minutes about this concept and your video totally cleared things up. Thank you!

  2. Garima says:

    yeah! really,
    you nailed it!

  3. Ujjwal Kumar Jha says:

    They din't teach us Calculus at school and began with this right away. Is it normal or it's the educational system here that's flawed?

  4. Amonthep Thongsin says:

    This is really great!!! Thank you.

  5. Lucas Sharon says:

    amazing video, one of the best of the khan academy(they do have awesome videos

  6. Nathan Willimzik says:

    Make and Edit to your Video on Sir Isaac Newton and Gottfried Wilhelm Leibniz being the inventors of calculus. (Thank you.)

    What? What? What? Your statement is flawed? Newton was not the sole inventor of calculus! Lets not forget Gottfried Wilhelm Leibniz. And how is this not calculus, calculus is partly a series of statements that defines the gradient in a point as that is what you are discussing isn't it, also your first tip would be obvious (if you have the instantaneous velocity information then yes calculus becomes obsolete in use for calculating gradient on the first derivative, (which you could express the full story in a simple function from which the gradient could be calculated without using the whole graph of the information), its just perfect). Yes you could find the area under the graph using the principle of Cavalieri (might be nice to add this to your video/as a simplified method of doing what is done in calculus to find the area true not needed for instantaneous). But how else do you think it was figured out. Back to the original statement. Please add a message excusing your mistake of Newton being "the inventor of calculus" which precludes any other inventors. May I point out the Newton-Leibniz Controversy.
    However, I must compliment you on your simple and fast explanation of the infinitesimal. Nice mentioning the ideas of the Zeno of Elea. But please add a small comment on Leibniz being included, it is important; and since you are catering to audiences that are possibly non-Britain or nationalistic to Britain. Wouldn't it make sense to include Leibniz, as they were the only side that were ever against Leibniz's calculus.

    Blame the guy that sent me this video so I could start this statement. Sorry.

  7. saeed ali says:

    mann i would be a sicentist if you were my teacher i would love phyiscs as my mother

  8. Haman Alawadhi says:

    That was perfect.

  9. mohmd252 says:

    I'm gonna to teach this forr my students lol

  10. Saniya Mulla says:

    awesome !! very well explained 🙂

  11. Gian Garde says:

    Is average speed synomous to velocity? I don't know.

  12. Tim Hitchins says:

    Hu, what about Leibniz?

  13. Eleetsole says:


  14. Alduin, Firstborn of Akatosh says:

    This is amazing! I can't believe people also did this: "_____ wouldn't give up, so I'm not giving up either!"

  15. Prince Kashyap says:

    I want you as my teacher

  16. DragonCorn says:

    Yo check out my mixtape

    SoundCloud: BigFishStickBoi

  17. Fissle Wine says:

    How would I work out instantaneous accelleration using this same example?

  18. Jeevan Ram says:

    What a Cool and Awesome Video.
    Great Job!

  19. Prathibha Siriyannavar says:


  20. 27kdon says:

    Newton walks into the room of squabbling physicists: He picks up the mic.. "Calculus bitches.." – epic mic drop

  21. excited inspired says:

    this is what I got: for a very very very small interval of time "dt" the very very very small distance covered by object is "dx" then if object will continue motion for another 1 second of time than the distance covererd is the instantaneous velocity of the object.whereas for a time interval of t seconds the distance covered by object is d than distance covered in one second by the object is the average velocity of the object!! huh

  22. Lana Banana says:




  24. Ketan Khobragade says:


  25. MD. Tanjilur Rahman says:

    sir, suppose if velocity of a bullet reduced to half then what will be the situation of the acceleration ????
    will it be remain same or it will also decrease ????

  26. Ray Osman says:

    It's my fifth time and I am watching this cool shortly explained video! I am having a test tomorrow, so I wandered instead of reading my book and summarize this topic, why not look again at this video? Well! I did revise this whole bunch of complicated topic with just this video! Thanks a lot! 😜

  27. Ray Osman says:

    I will watch this video again and again :-))

  28. Ahmed Siddiq Khan says:

    #Fantaboulous sir just explain limit why it approaches to zero….

  29. midgint says:

    Actually it was Liebniz that invented Calculus :^)

  30. Fartuun Ismail says:

    thanks so much

  31. everyone's tube says:

    thank you sooooo muchhh…..

  32. Seerat Fatima says:

    At last after four years, now i got the concept of instantaneous velocity. LOL

  33. Purge says:

    Bravo 4min & 38 seconds its all clear… Where as my teacher took 40 minutes but still….. Thanks

  34. Balkaran says:

    I thought that they collaborated with minute physics

  35. Dominus Icarus says:

    Isn't 5m/s that it takes to go to your home that is distant 1000m and 200 seconds to take your average speed and not velocity since those values are scalar and no direction nor unit vector involved?

  36. Anshal Kapil says:

    Thank you so much!!

  37. rockstar yo yo says:

    cool accent 😀😁😁😁😝

  38. Siyanda Jama says:


  39. Reyna says:

    LOL at "pretend" you're a physics student. Like who else would be researching these videos beside mainly physics students?

  40. Colby Fong says:

    I wish I could run at 24 m/s

  41. david milse says:

    Look the new formula for photon's energy  on the SALEH THEORY group's youtube chanel:
    Saleh Theory-com

  42. Post Melon says:

    let me save ur time. he starts teaching at 3:35. np

  43. teklu mahari says:

    o didn't to lose but you kept me in save

  44. Sa Sa says:


  45. King Som says:


  46. King Som says:

    for this good video

  47. exam near says:

    u clear all my doubt
    thnk u sooooo much

  48. Gary4 DLC says:

    So … the instantaneous velocity of an object can be negative during a specific moment on a time interval, despite the average velocity being positive???

  49. Pablo Pena says:


  50. shanmuga sundari says:

    nice video great and short explanation

  51. Milind Angal says:

    4 minutes and 4 days….huge diff in this and my school

  52. Asma Arshad says:

    Very nice understanding skills ………plz tell instantaneous velocity in terms of circular motion

  53. Adina Zahid says:

    Awesome Boy 😀💖👍

  54. Adina Zahid says:

    Can any one solve this problem?
    A car moves with a speed of 40 kmh^-1 for the first half time and with a speed of 60 km/h for the second half time. What is averge speed during while journy?

  55. Johnny black says:

    whats the name of the song that plays

  56. Tarun Siva nantham says:

    Thank you sir

  57. praeyden says:

    this beat lit

  58. Noran Felemban says:

    Thank youuu

  59. ONLINER Gaming says:

    Sir I can't understand graph

  60. Siddhesh says:

    This was so easy, why dont teachers teach us like this..

  61. Tarun Oorloff-Kay says:

    this video makes me depressed do not rekamend

  62. sanjiv mahato says:

    His explanation was very clear. Loved this video

  63. Ps4 N1nja says:

    What my teacher cant teach me in 4 hours inn 4 minutes

  64. Fraser Souris says:

    Ancient Greeks: The best Overthinkers

  65. Study For Students 49 says:

    আমার চ্যানেলে পলিটেকনিকের ভিডিও আপলোড করা হয়ে থাকে

  66. artsy sketches says:

    ⓦⓐⓣⓒⓗⓘⓝⓖ ⓣⓗⓘⓢ ⓕⓞⓡ ⓐⓝ ⓔⓧⓐⓜ ⓦⓘⓢⓗ ⓜⓔ ⓛⓤⓒⓚ😭😀😭😀

  67. SUBRA says:

    Awesome can you please upload instantaneous acceleration

  68. Xrmion 2 says:

    i Wish I had a teacher Like him LOL

  69. naresh rathna says:

    Great class

  70. Amsu Nath says:

    U r awesome man

  71. Esteban says:

    I wish they didn't put background music into it. It's distracting and bothersome when playing at fast speeds. Please don't do this anymore. Keep with the khan methodology for videos. Thanks. Great work, but sh*t background music.

  72. S. N. Oza says:

    plz understand in hindi

  73. Sabhyata Bhattari says:


  74. Muhammed Jimale says:


  75. Ella Playz says:

    I can’t understand anything

  76. bob do something says:

    Who is captain antares???

  77. Iridescent Heart says:

    great awesome keep it up keep going awesome video thanks alot

  78. Adam Shaban says:

    ok, now this is epic

  79. Brax says:

    that star wars analogy is too accurate

  80. Dave Humphreys says:

    I would disagree with you [ at 2:47] when you say that 'an infinitesimally small distance/ an infinitesimally small time' = 0/0. NO IT DOESN'T!! An infinitesimally small distance STILL has a start point and an end point. An infinitesimally short time interval STILL has a start time and an end time, ie a duration. NEITHER of these quantities are zero therefore their ratio is NOT 0/0!!

  81. McKenzie P says:

    someone just please kill me.

  82. Chinedu Atisele says:

    That. Was. Good.

  83. Prakash Chadra Dey says:

    Well will there be a speed when the time interval is zero ?

  84. Prakash Chadra Dey says:

    Well will there be a speed when the time interval is zero ?

  85. mahendra mathur says:

    Well enough but it didn't help me out.

  86. Yosef Tigabu says:

    Wow cool dude that was so simplified men kepp it up

  87. Malk Khaled says:

    really you are a great teacher

  88. The Changster says:

    thank you

  89. FUCK SAND says:

    what a terrible physics student, he should be doing the massive amount of homework he obviously has, not watching tv or a movie

    …he must be me

  90. BASEsick TRUTH says:

    Shouldn't all the instantaneous velocities have +/- signs in front of them since they are vectors?

  91. Sergio K says:

    Shame to those 126 dislikes, this video was amazing, perfectly understood what I couldn't in a 2 hours class, Thanks for the amazing work.

  92. Gaming Zone says:

    The best Video at youtube on this topic

  93. moaaz bhnas says:

    Thank you <3

  94. Richard Dickson says:

    lord, he ran at 28.8 kmph at the end

    the motivation is real people

  95. Hamoood 8898 says:

    amazing 😉
    and how this was easy in high school but now at college it’s hard ?

  96. Apeksha G says:

    Wow thank you!! This is amazing!!

  97. Abdullah Mursal says:

    I need help to the calculus? Function, limit, graphic and instantaneous.👷🏻‍♂️

  98. Movil Net says:


  99. gary mcleod says:

    Cleared up some points I 've struggled with. I'm glad I donate to Kahn Academy.

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