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Sebuah benda mula-mula diam lalu bergerak dengan kecepatan awal v 0 ​ ​ = ( 6 i + 4 j ​ ) m / s . Elektron tersebut kemudian dipercepat dengan persamaan a = ( ( 2 t + 2 ) i + ( 6 − 2 t ) j ​ ) m / s 2 .Jika t dalam s, v dalam m/s, dan a dalam m / s 2 ,tentukan: kecepatan elektron saat t = 1 s ; perpindahan saat t = 3 s .

Sebuah benda mula-mula diam lalu bergerak dengan kecepatan awal . Elektron tersebut kemudian dipercepat dengan persamaan . Jika  dalam s,  dalam m/s, dan  dalam , tentukan:

  1. kecepatan elektron saat ;
  2. perpindahan saat .space

space 

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U. Amalia

Master Teacher

Mahasiswa/Alumni Universitas Islam Negeri Sunan Gunung Djati Bandung

Jawaban terverifikasi

Jawaban

jawabannya adalah :

jawabannya adalah : 

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Pembahasan

Diketahui : Ditanyakan : kecepatan elektron saat ; perpindahan saat . Jawab Kecepatan elektron saat Perpindahan saat Oleh karena itu, jawabannya adalah :

Diketahui : 
begin mathsize 14px style stack v subscript 0 with rightwards arrow on top equals open parentheses 6 space i with hat on top plus 4 space j with hat on top close parentheses space straight m divided by straight s end style

begin mathsize 14px style a with rightwards arrow on top equals open parentheses open parentheses 2 t plus 2 close parentheses space i with hat on top plus open parentheses 6 minus 2 t close parentheses space j with hat on top close parentheses space straight m divided by s squared end style

Ditanyakan : 

  1. kecepatan elektron saat undefined;
  2. perpindahan saat undefined.space

Jawab

Kecepatan elektron saat  begin mathsize 14px style t equals 1 space straight s end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell v with rightwards arrow on top end cell equals cell integral a with rightwards arrow on top d t end cell row blank equals cell integral open parentheses open parentheses 2 t plus 2 close parentheses space i with hat on top plus open parentheses 6 minus 2 t close parentheses space j with hat on top close parentheses d t end cell row blank equals cell open parentheses t squared plus 2 t close parentheses space i with hat on top plus open parentheses 6 t minus t squared close parentheses space j with hat on top plus v subscript 0 end cell row blank equals cell open parentheses t squared plus 2 t close parentheses space i with hat on top plus open parentheses 6 t minus t squared close parentheses space j with hat on top plus 6 space i with hat on top plus 4 space j with hat on top end cell row blank equals cell open parentheses t squared plus 2 t plus 6 close parentheses space i with hat on top plus open parentheses negative t squared plus 6 t plus 4 close parentheses space j with hat on top end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell v with rightwards arrow on top left parenthesis 1 right parenthesis end cell equals cell open parentheses 1 squared plus 2.1 plus 6 close parentheses space i with hat on top plus open parentheses negative left parenthesis 1 squared right parenthesis plus 6.1 plus 4 close parentheses space j with hat on top end cell row blank equals cell open parentheses 9 space i with hat on top plus 9 space j with hat on top close parentheses space straight m divided by straight s end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar v with rightwards arrow on top left parenthesis 1 right parenthesis close vertical bar end cell equals cell square root of 9 squared plus 9 squared end root end cell row blank equals cell square root of 81 plus 81 end root end cell row blank equals cell square root of 162 end cell row blank equals cell 9 square root of 2 space straight m divided by straight s end cell end table end style 

Perpindahan saat undefined 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell r with rightwards arrow on top end cell equals cell integral v with rightwards arrow on top d t end cell row blank equals cell integral open parentheses open parentheses t squared plus 2 t plus 6 close parentheses space i with hat on top plus open parentheses negative t squared plus 6 t plus 4 close parentheses space j with hat on top close parentheses d t end cell row blank equals cell open parentheses open parentheses 1 third t cubed plus t squared plus 6 t close parentheses space i with hat on top plus open parentheses negative 1 third t cubed plus 3 t squared plus 4 t close parentheses space j with hat on top close parentheses space straight m end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell r with rightwards arrow on top left parenthesis 3 right parenthesis end cell equals cell open parentheses 1 third open parentheses 3 cubed close parentheses plus 3 squared plus 6.3 close parentheses space i with hat on top plus open parentheses negative 1 third open parentheses 3 cubed close parentheses plus 3.3 squared plus 4.3 close parentheses space j with hat on top end cell row blank equals cell open parentheses 36 space i with hat on top plus 30 space j with hat on top close parentheses space straight m end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar r with rightwards arrow on top left parenthesis 3 right parenthesis close vertical bar end cell equals cell square root of 36 squared plus 30 squared end root end cell row blank equals cell square root of 1296 plus 900 end root end cell row blank equals cell square root of 2196 end cell row blank equals cell 6 square root of 61 space straight m end cell end table end style  

Oleh karena itu, jawabannya adalah : 

  1. bold italic v subscript begin bold style left parenthesis 1 right parenthesis end style end subscript bold equals bold space bold 9 square root of bold 2 bold space bold m bold divided by bold s bold space
  2. Error converting from MathML to accessible text.blank

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