KINEMATIKA

▶ Persamaan Posisi, Kecepatan, Percepatan

Partikel bergerak dengna persamaan kecepatan v(t) = 4t³ + 6t² + 1

a ][

r(t) = __ ?

r(t) = ∫ v(t) dt

r(t) = ∫ (4t³ + 6t² + 1) dt

r(t) = t⁴ + 2t³ + t + C

saat t = 0 , r = 0 ➡ C = 0

r(t) = t⁴ + 2t³ + t ✔

b ][

r(1) = __ ?

r(1) = 1⁴ + 2(1)³ + 1

r(1) = 4 satuan jarak ✔

c ][

r(2) = __ ?

r(2) = 2⁴ + 2(2)³ + 2

r(2) = 34 satuan jarak ✔

d ][

v.rt = __ ?

v.rt = ∆r / ∆t

v.rt = (34 - 4) / (2 - 1)

v.rt = 30 satuan kecepatan ✔

e ][

v(1) = __ ?

v(1) = 4(1)³ + 6(1)² + 1

v(1) = 25 satuan kecepatan ✔

f ][

v(3) = __ ?

v(3) = 4(3)³ + 6(3)² + 3

v(3) = 165 satuan kecepatan ✔

g ][

a.rt = __ ?

a.rt = ∆v / ∆t

a.rt = (165 - 25) / (3 - 1)

a.rt = 70 satuan percepatan ✔

h ][

a(t) = __ ?

a(t) = d v(t) / dt

a(t) = d (4t³ + 6t² + 1) / dt

a(t) = 12t² + 12t ✔

i ][

a(1) = __ ?

a(1) = 12(1)² + 12(1)

a(1) = 24 satuan percepatan ✔

j ][

a(2) = __ ?

a(2) = 12(2)² + 12(2)

a(2) = 72 satuan percepatan ✔