Answer:
x = -1, x = 1
Step-by-step explanation:
Factor the equation. (It's a difference of squares, so we know the form will be (a-b)(a+b).)
Test this by FOILing it out, if you're unsure. This is something it can be good to memorize!
Set it equal to 0.
Separate the two parenthetical expressions by the Zero Product Property.
Solve for x!
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