Roboguru

Pertanyaan

Persamaan posisi sebuah partikel yang bergerak dalam bidang adalah r with rightwards arrow on top equals left parenthesis 4 t squared plus 2 t right parenthesis straight i with hat on top plus left parenthesis 3 t squared plus 3 t right parenthesis straight j with hat on top  dengan r dalam meter dan t dalam sekon. Kecepatan rata-rata partikel dalam selang waktu 1 s sampai 2 s adalah ....space 

  1. 14 i with hat on top space plus space 12 j with hat on top space

  2. 13 i with hat on top space plus space 12 j with hat on top space

  3. 7 i with hat on top space plus space 6 j with hat on top space

  4. 6 i with hat on top space plus space 6 j with hat on top 

  5. 6 i with hat on top space plus space 7 stack j space with hat on top

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang paling tepat adalah A.  

Pembahasan

Diketahui:

straight r with rightwards arrow on top equals left parenthesis 4 straight t squared plus 2 straight t right parenthesis straight i with hat on top plus left parenthesis 3 straight t squared plus 3 straight t right parenthesis straight j with hat on top

Ditanyav with bar on top saat t = 1 s dan t = 2 s ?

Penyelesaian:

Kecepatan rata-rata adalah perubahan posisi tiap selang waktu tertentu dan dapat dinyatakan dengan persamaan berikut

v with bar on top equals fraction numerator capital delta r with rightwards arrow on top over denominator capital delta t end fraction equals fraction numerator capital delta x with rightwards arrow on top bold i with bold hat on top plus capital delta y with rightwards arrow on top bold j with bold hat on top over denominator capital delta t end fraction equals fraction numerator capital delta x with rightwards arrow on top over denominator capital delta t end fraction bold i with bold hat on top plus fraction numerator capital delta y with rightwards arrow on top over denominator capital delta t end fraction bold j with bold hat on top equals stack v subscript x with rightwards arrow on top bold i with bold hat on top plus v with rightwards arrow on top subscript y bold j with bold hat on top 

Posisi partikel saat t = 1 s adalah

r with rightwards arrow on top left parenthesis 1 right parenthesis equals left parenthesis 4 t squared plus 2 t right parenthesis bold i with bold hat on top plus left parenthesis 3 t squared plus 3 t right parenthesis bold j with bold hat on top r with rightwards arrow on top left parenthesis 1 right parenthesis equals left parenthesis 4 left parenthesis 1 right parenthesis squared plus 2 left parenthesis 1 right parenthesis right parenthesis bold i with bold hat on top plus left parenthesis 3 left parenthesis 1 right parenthesis squared plus 3 left parenthesis 1 right parenthesis right parenthesis bold j with bold hat on top r with rightwards arrow on top left parenthesis 1 right parenthesis equals left parenthesis 6 right parenthesis bold i with bold hat on top plus left parenthesis 6 right parenthesis bold j with bold hat on top   

Posisi partikel saat t = 2 s adalah

r with rightwards arrow on top left parenthesis 2 right parenthesis equals left parenthesis 4 t squared plus 2 t right parenthesis bold i with bold hat on top plus left parenthesis 3 t squared plus 3 t right parenthesis bold j with bold hat on top r with rightwards arrow on top left parenthesis 2 right parenthesis equals left parenthesis 4 left parenthesis 2 right parenthesis squared plus 2 left parenthesis 2 right parenthesis right parenthesis bold i with bold hat on top plus left parenthesis 3 left parenthesis 2 right parenthesis squared plus 3 left parenthesis 2 right parenthesis right parenthesis bold j with bold hat on top r with rightwards arrow on top left parenthesis 2 right parenthesis equals left parenthesis 20 right parenthesis bold i with bold hat on top plus left parenthesis 18 right parenthesis bold j with bold hat on top 

Kecepatan rata-rata partikel dalam selang waktu 1 s sampai 2 s adalah

v with bar on top equals fraction numerator capital delta r with rightwards arrow on top over denominator capital delta t end fraction v with bar on top equals fraction numerator left parenthesis 20 bold i with bold hat on top plus 18 bold j with bold hat on top right parenthesis minus left parenthesis 6 bold i with bold hat on top plus 6 bold j right parenthesis over denominator 2 minus 1 end fraction v with bar on top equals fraction numerator 14 bold i with bold hat on top plus 12 bold j with bold hat on top over denominator 1 end fraction v with bar on top equals 14 bold i with bold hat on top plus 12 bold j with bold hat on top  

Sehingga kecepatan rata-rata partikel dalam selang waktu 1 s sampai 2 s adalah 14 i with hat on top space plus space 12 j with hat on top space

Oleh karena itu, jawaban yang paling tepat adalah A.  

1rb+

5.0 (3 rating)

Pertanyaan serupa

Suatu partikel mula-mula berada di pusat koordinat, kemudian bergerak dengan persamaan posisi r=(6t2+4)i+(8t+3)j​ m. Besar kecepatan rata-rata partikel dalam selang waktu 0 s sampai 1 s adalah ....

1rb+

4.0

Jawaban terverifikasi

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