JAWABAN UJI KOMPETENSI KINEMATIKA GERAK LURUS

KELAS : XI IPA 1

KODE : A

1. dan (5)
   

   r = (6t² – 2t – 5)i + (3t² – 5t + 1)j
   

   1. v = dr/dt = (12t – 2)i + (6t – 5)j
      

      t = 1 ® v = 10i + j
      

      v = Ö101 m/s
      

   2. a = dv/dt = 12i + 6j
      

      a = Ö180
      

2. dan (6)
   

   a = 4i + 6j
   

   v₀ = i +3j
   

   v = v₀ + ò a .dt
   

   = (i + 3j) + (4t i + 6t j)
   

   = (4t +1) i + (6t+3)j
   

   = 13i + 21j
   

   v = Ö610 m/s
   

3. dan (7)
   

   r = (4t – 2) i + (2 – 3t) j
   

   1. t₁ = 2 Þ r₁ = 6 i – 4 j m
      

      t₂ = 4 Þ r₂ = 14 i – 10 j m
      

      v_r = {(14 i – 10 j) – (6 i – 4 j)}/2
      

      = 4 i – 3 j m/s
      

   2. v = dr/dt = 4 i – 3 j m/s
      
4. dan (8)
   

   r₀ = 3 i + 4 j
   

   v = (4t + 3) i + (8t – 6) j
   

   1. r = r₀ + ò v dt
      

      = (3 i + 4 j) + ò(4t + 3) i + (8t – 6) j dt
      

      = (3 i + 4 j) + (2t² + 3t) i + (4t² – 6t) j
      

      = (2t² + 3t + 3) i + (4t² – 6t + 4) j
      

      = (2.2² + 3.2 + 3) i + (4.2² – 6.2 + 4) j
      

      = 17 i + 8 j meter
      

   2. a = dv/dt = 4 i + 8 j m/s²
      

 

 

 

 

 

 

KODE B :

1. dan (5)
   

   r₀ = i + 5 j
   

   v = (6t -2) i + (8 – 2t) j
   

   1. a = dv/dt = 6 i – 2j
      
   2. r = r₀ + ò v dt
      

      = (i + 5j) + ò(6t – 2) i + (8 – 2t) j dt
      

      = (i + 5j) + (3t² – 2t) i + (8t – t²) j
      

      = (3t² – 2t + 1) i + (8t – t² + 5) j
      

      = 2 i + 12 j
      

2. dan (6)
   

   r = (4 – 6t) i + (4 – 2t) j
   

   1. t₁ = 2 Þ r₁ = (4 – 6.2) i + (4 – 2.2) j = - 8 i
      

      t₂ = 4 Þ r₂ = (4 – 6.4) i + (4 – 2.4) j = - 20 i – 4 j
      

      v_r = {(- 20 i – 4 j) – (-8 i)}/2 = - 6 i – 2 j
      

   2. v = dr/dt = -6 i – 2 j
      
3. dan (7)
   

   r = (5t² – 7t + 4) i + (2t² – 5t – 2) j
   

   1. v = dr/dt = 23 i + 7 j
      

      = Ö578 m/s
      

   2. a = dv/dt = 10 i + 4 j
      

      a = Ö116 m/s²
      

4. dan (8)
   

   v₀ = 5 i + j
   

   a = 7 i + 5 j
   

   v = v₀ + ò a . dt
   

   = (5 + 7t) i + (1 + 5t) j
   

   = (5 + 7.2) i + (1 + 5.2) j
   

   = 19 i + 11 j
   

   v = Ö482 m/s