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1 answer:
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Answer:
a. v(t)= -6.78 + 16.33 b. 16.33 m/s
Step-by-step explanation:
The differential equation for the motion is given by mv' = mg - γv. We re-write as mv' + γv = mg ⇒ v' + γv/m = g. ⇒ v' + kv = g. where k = γ/m.Since this is a linear first order differential equation, We find the integrating factor μ(t)= =
. We now multiply both sides of the equation by the integrating factor.
μv' + μkv = μg ⇒ v' + k
v = g
⇒ [v
]' = g
. Integrating, we have
∫ [v]' = ∫g
v =
+ c
v(t)= + c
.
From our initial conditions, v(0) = 9.55 m/s, t = 0 , g = 9.8 m/s², γ = 9 kg/s , m = 15 kg. k = y/m. Substituting these values, we have
9.55 = 9.8 × 15/9 + c = 16.33 + c
c = 9.55 -16.33 = -6.78.
So, v(t)= 16.33 - 6.78. m/s = - 6.78
+ 16.33 m/s
b. Velocity of object at time t = 0.5
At t = 0.5, v = - 6.78 + 16.33 m/s = 16.328 m/s ≅ 16.33 m/s
15.
Add "g" on both sides
Multiply 5 on both sides to get x by itself
x = 5(a + g)
x = 5a + 5g
18. a = 3n + 1
Subtract 1 on both sides
a - 1 = 3n
Divide 3 on both sides to get n by itself
= n
21. M = T - R
Add "R" on both sides to get "T" by itself
M + R = T
24. 5p + 9c = p
Subtract "5p" on both sides
9c = p - 5p
9c = -4p
Divide 9 on both sides to get "c" by itself
c = or c =
27. 4y + 3x = 5
Subtract "4y" on both sides
3x = 5 - 4y
Divide 3 on both sides to get "x" by itself
x =
x =