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a(t) = 16t² m/det²
Jawab :
a) kecepatan saat t = 6
Vt = Vo + ∫at
Vt = 0 + 16/3 t³
Vt = 16/3 (6)³
Vt = 1152 m/det
b) Persamaan gerak
r(t) = ro + ∫vt
r(t) = ro + 4/3 t^4
r(2) = ro + 4/3 (2)^4
1 = ro + 4/3 (16)
ro = - 20,3333
persaman gerak
r(t) = { - 20,3333 + 4/3 t^4 } m
c) Kecepatan benda setelah menempuh jarak 66,16 m
r(t) = { - 20,3333 + 4/3 t^4 } m
66,16 m = { -20,3333 + 4/3 t^4 } m
4/3 t^4 = 66,16 + 20,3333
4/3 t^4 = 86,4933
t^4 = 3/4 x 86,4933
t^4 = 64,87
t = 2,838
Maka, kecepatan sesaat :
V(t) = 16/3 t³
V(2,838) = 16/3 (2,838)³
V(2,838) = 121,9090 m/det