Motion graphs:Area Under Graph Explanation - IGCSE Physics

00:07:02
https://www.youtube.com/watch?v=y4xOBx-vh7o

Resumo

TLDRI videon förklaras hur man beräknar arean av rektanglar, trianglar och trapezium med hjälp av en kartesisk plan. Rektanglar beräknas med formeln längd gånger bredd, medan trianglar använder hälften av basen gånger höjden. Trapezium kan delas upp i två delar för att beräkna arean. Det betonas att alla formler, förutom cirkelns, baseras på rektangelns formel. Exempel ges på hur man beräknar area under en hastighet-tid graf.

Conclusões

  • 📏 Arean av en rektangel = längd × bredd
  • 🔺 Arean av en triangel = 1/2 × bas × höjd
  • 🔶 Arean av en trapezium = 1/2 × (a + b) × höjd
  • 📊 Kartesisk plan = x- och y-axel
  • 🕷️ René Descartes och den kartesiska planen
  • 📐 Trianglar är hälften av rektanglar
  • ✂️ Dela upp trapezium för enklare beräkning
  • 📈 Hastighet-tid graf visar sträcka
  • 🧮 Många formler baseras på rektangelns formel
  • 🔍 Höjd kan vara lutad i trapezium

Linha do tempo

  • 00:00:00 - 00:07:02

    I denna del av videon förklaras hur man beräknar arean av olika geometriska figurer, inklusive rektanglar, trianglar och trapezium. Först introduceras det kartesiska planet, där x- och y-axlar används för att placera figurer. Arean av en rektangel beräknas genom att multiplicera längden med bredden. När det gäller en rätvinklig triangel, används formeln hälften av basen gånger höjden, eftersom triangeln är hälften av en rektangel. För trapezium används formeln hälften av summan av de parallella sidorna gånger höjden. Det betonas att alla dessa formler, förutom cirkelns, bygger på rektangelns formel.

Mapa mental

Vídeo de perguntas e respostas

  • Hur beräknar man arean av en rektangel?

    Arean av en rektangel beräknas genom att multiplicera längden med bredden.

  • Vad är formeln för att beräkna arean av en triangel?

    Arean av en triangel beräknas som hälften av basen multiplicerat med höjden.

  • Hur beräknar man arean av en trapezium?

    Arean av en trapezium beräknas som hälften av summan av de parallella sidorna multiplicerat med höjden.

  • Vad är en kartesisk plan?

    En kartesisk plan är ett koordinatsystem med en x-axel och en y-axel.

  • Varför halverar vi basen i trianglar?

    Vi halverar basen eftersom vi beräknar arean av en triangel, som är hälften av en rektangel.

  • Vad är skillnaden mellan en rektangel och en trapezium?

    En rektangel har fyra räta vinklar och parallella sidor, medan en trapezium har endast ett par parallella sidor.

  • Kan man använda samma formler för olika geometriska figurer?

    Ja, många formler för olika figurer baseras på rektangelns formel.

  • Vad är ett exempel på en graf som kan representera area?

    En hastighet-tid graf kan representera area under kurvan som motsvarar sträcka.

  • Hur kan man dela upp en trapezium för att beräkna arean?

    En trapezium kan delas upp i en triangel och en rektangel för att förenkla beräkningen av arean.

  • Vad är en hastighet-tid graf?

    En hastighet-tid graf visar hur hastigheten förändras över tid och kan användas för att beräkna sträcka.

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Legendas
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Rolagem automática:
  • 00:00:00
    let's do that while we've got nobody
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    else's questions let's just explain that
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    okay so
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    how would you get an area of a rectangle
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    okay
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    now if i put that
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    on a cartesian plane
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    it's still a rectangle
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    okay we call this thing a cartesian
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    plane
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    that that whole thing where we have the
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    x and y axis
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    french mathematician rene de cartes
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    figured out
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    while lying on his bed one day he was
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    actually a lawyer not a mathematician
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    and there was a little spider on the
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    roof
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    and he thought
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    if i divide it in a horizontal and a
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    vertical distance i can calculate
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    exactly how far that spider is from the
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    corner of the ceiling and that's where
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    he got it cartesian plane rene de cartes
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    so we put it on a cartesian plane an x
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    and a y
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    axis
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    it's still a rectangle
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    so we still use length times breath
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    okay so sometimes it's not a full
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    rectangle
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    it looks like this
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    like with the velocity time graph
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    now where that line ends
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    that is the time okay so that
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    is going to be my base from here to
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    there
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    and that's going to be my width or with
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    length whatever you call it length times
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    breath
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    make that length times breath whatever
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    your formula is i'm going to times this
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    by this because it's a rectangle
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    now
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    if
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    i have a triangle
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    let's start with a right angle triangle
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    how do i calculate the area of a right
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    angle triangle let's ask
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    ali
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    i'll let you muted
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    yay
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    ali doesn't want to help us
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    let's ask mira
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    teach it's
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    half base times height
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    okay half
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    of the base times the height
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    okay
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    now
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    why do we half it because actually we're
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    calculating a rectangle
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    breadth
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    times height
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    but it's not a whole rectangle it's half
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    of a rectangle so it's half breath times
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    height because it's actually a triangle
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    okay so now if we put this on a
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    cartesian plane x and y axis
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    okay
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    we take this value from here to there so
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    let's say that's zero and that's five
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    and that goes up to four zero and four
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    so that's gonna be five
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    and four
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    so half times five times four
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    and then i get the area underneath the
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    graph now
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    a lot of the times you're not going to
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    have that you're just going to have a
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    diagonal line
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    so if my diagonal line ends here
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    i get my
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    value here and i measure from there to
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    there and i get my value here and i
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    measure from there to there okay the
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    last one that i want to show you guys
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    is a trapezium now you can simply divide
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    a trapezium into two parts
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    okay
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    if i have a trapezium like this
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    okay
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    um
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    who knows that formula for the area of a
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    trapezium
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    half a plus b times height
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    a
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    well like top times bottom
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    the height okay now guys be careful
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    because
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    height
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    doesn't always have to look like that
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    sorry that was my board marker okay
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    height can also be like this
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    okay half of the parallel sides now
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    which two sides are parallel that one
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    and that one
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    okay so if that's two and that's six
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    it's two plus six half of that
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    okay
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    and then times the height
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    okay so why would we half it
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    okay
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    if we took
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    the full two plus six
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    we actually get this
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    okay if that's two and that's six we
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    actually get to a rectangle again
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    so
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    it is actually
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    half of a rectangle
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    every single formula except for a circle
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    is based on the formula of a rectangle
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    okay
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    so
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    half base times height
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    just remove that
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    the height in this case is this length
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    over here let's make that five so half
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    base times height is half
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    of
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    two plus six it's eight times five
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    forty times half is twenty so that area
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    would be twenty
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    now i place this
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    on a cartesian plane and it looks like
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    this
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    okay this is a velocity time graph
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    the guy starts from two
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    he goes up to five
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    well let's make it six
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    in
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    five seconds
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    okay
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    so i could
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    calculate it as a trapezium that's six
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    this is two and that is five so half of
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    six plus two times five or because i'm
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    lazy i like doing this
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    i split it up into a triangle
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    okay when i do that
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    if this is two and that's another
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    increment so that height is then four
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    from here to there becomes four
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    the base is still five
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    so then the top part is going to be half
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    of
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    four times five is ten
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    and the bottom part
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    is going to be two times five length
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    times breath
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    two times five
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    is ten so the whole area under the graph
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    is ten
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    ten plus ten twenty
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    okay
Etiquetas
  • area
  • rektangel
  • triangel
  • trapezium
  • kartesisk plan
  • formler
  • geometri
  • hastighet-tid graf
  • beräkning
  • matematik