Question

persaman diferensial soal berikut ​

Answer 1

Jawaban:

A.

v(t) = ∫ a(t) dt

v(t) = ∫ (2t+3)³ dt

v(t) = (∫ 8t³ dt) + (∫ 36t² dt) + (∫ 54t dt) + c

v(t) = 2t⁴ + 12t³ + 27t² + c

Dik: v(0) = 4 m/s

4 = 2(0)⁴ + 12(0)³ + 27(0)² + c

c = 4

v(t) = 2t⁴ + 12t³ + 27t² + 4

v(3) = 2(3)⁴ + 12(3)³ + 27(3)² + 4

= 198 m/s

B.

v_rata_rata = (v(t) + v(0))/2

v_rata_rata = (2t⁴ + 12t³ + 27t² + 4 + 4)/2

v_rata_rata = t⁴ + 6t³ + 13,5t² + 2

S = ∫ v_rata_rata dt

S = (∫ t⁴ dt) + (∫ 6t³ dt) + (∫ 13,5t² dt) + (∫ 2 dt)

S = t⁵/5 + 3t⁴/2 + 4,5t³ + 2t

S(3) - S(0)= (3⁵/5 + 3³/2 + 4,5(3)³ + 2(3)) - (0⁵/5 + 3⁴/2 + 4,5(0)³ + 2(0))

S = 176,25 m