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Benda bergerak dengan persamaan posisi r = ( 4 t + 5 ) i + ( 6 t 2 − 4 t ) j ​ , r dalam meter dan t dalam sekon. Berdasarkan persamaan tersebut, tentukan: a. posisi benda saat t = 2 s ; b. persamaan kecepatan; c. besar kecepatan saat ; d. persamaan percepatan; e. besar percepatan saat t = 3 s .

Benda bergerak dengan persamaan posisi  dalam meter dan  dalam sekon. Berdasarkan persamaan tersebut, tentukan:

a. posisi benda saat ;

b. persamaan kecepatan;

c. besar kecepatan saat undefined;

d. persamaan percepatan;

e. besar percepatan saat .

  1. (...)undefined 

  2. (...)undefined 

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R. Sobirin

Master Teacher

Mahasiswa/Alumni Universitas Indonesia

Jawaban terverifikasi

Pembahasan

a. Posisi benda saat : b. Persamaan kecepatan: c. besar kecepatan saat : d. Persamaan percepatan: e. Besar percepatan saat :

a. Posisi benda saat begin mathsize 14px style t equals 2 space straight s 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 2 right parenthesis end cell equals cell open parentheses 4.2 plus 5 close parentheses space i with hat on top plus open parentheses 6.2 squared minus 4.2 close parentheses space j with hat on top end cell row blank equals cell open parentheses 13 space i with hat on top plus 16 space j with hat on top close parentheses space straight m end cell end table end style  

b. Persamaan kecepatan:

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 fraction numerator d r with rightwards arrow on top over denominator d t end fraction end cell row blank equals cell fraction numerator d over denominator d t end fraction open parentheses open parentheses 4 t plus 5 close parentheses space i with hat on top plus open parentheses 6 t squared minus 4 t close parentheses space j with hat on top close parentheses end cell row blank equals cell open parentheses 4 space i with hat on top plus open parentheses 12 t minus 4 close parentheses space j with hat on top close parentheses space straight m divided by straight s end cell end table end style 

c. besar kecepatan saat undefined:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell v with rightwards arrow on top left parenthesis 2 right parenthesis end cell equals cell 4 space i with hat on top plus open parentheses 12.2 minus 4 close parentheses space j with hat on top end cell row blank equals cell open parentheses 4 space i with bar on top plus 20 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 2 right parenthesis close vertical bar end cell equals cell square root of 4 squared plus 20 squared end root end cell row blank equals cell square root of 16 plus 400 end root end cell row blank equals cell square root of 416 end cell row blank equals cell 4 square root of 26 space straight m divided by straight s end cell end table end style 

d. Persamaan percepatan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell fraction numerator d v with rightwards arrow on top over denominator d t end fraction end cell row blank equals cell fraction numerator d over denominator d t end fraction open parentheses 4 space i with hat on top plus open parentheses 12 t minus 4 close parentheses space j with hat on top close parentheses end cell row blank equals cell 12 space j with hat on top space straight m divided by straight s squared end cell end table end style 

e. Besar percepatan saat begin mathsize 14px style t equals 3 space straight s end style:

begin mathsize 14px style a with rightwards arrow on top left parenthesis 3 right parenthesis equals 12 space j with hat on top space straight m divided by straight s squared end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top left parenthesis 3 right parenthesis close vertical bar end cell equals cell square root of 12 squared end root end cell row blank equals cell square root of 144 end cell row blank equals cell 12 space straight m divided by straight s squared end cell end table end style 

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