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# what is solution to mv' = -9.8m + kv with respect to t ? v(0)=v(0)?

a. v(t) = 9.8m/k + (v(0)+9.8m/k)e^(kt/m)

b. a. v(t) = 9.8m/k + (v(0) - 9.8m/k)e^(kt/m)

c. Neither

d.DNE

### 4 Answers

- Anonymous1 decade agoFavorite Answer
mv' - kv = - 9,8

This is a non homogen differential equation

You have to solve first the homogen differential equation:

mv' - kv = 0

mv' = kv

m dv/dt = k v

m dv/v = k/dt

int m dv/v = int k/dt

m ln v = kt

ln v = kt/m + C

v = e^kt/m + e^C = A e^kt/m

Now you have to calculate a particular solution from the non homogen differential equation and add both solutions.

mv' = - 9,8 + kv accepts v = B,

B a constant, as a particular solution

0 = - 9.8 + k. B

So, B = 9.8/k

Now add both solutions:

v = A e^kt/m + 9.8/k

And use the initial conditions: v(0) = v(0) to evaluate A

v(0) = A e^0 + 9.8/k

So, A = v(0) - 9.8/k

The solution is b. You mistyped it too.

Ana

- 1 decade ago
1) Rewrite in terms of dv/dt.

m(dv/dt) = -9.8m + kv

2) Rearrange so v and dv are on the same side. This is a separable differential equation.

[1/(kv - 9.8m)]dv = [1/m]dt

3) Integrate both sides

[ln(kv - 9.8m)]/k = (t/m) + C

4) ln(kv - 9.8m) = (tk/m) + C

5) kv - 9.8m = e^ [(tk/m) + C]

6) kv = Ce^ [tk/m] + 9.8m

7) v = [Ce^ [tk/m] + 9.8m]/k

I don't think this matches A or B, so C.

- 1 decade ago
v'=dv/dt

m(dv/dt)=-9.8m+kv

m(dv)=-9.8m(dt)+kv(dt)

take S as the symbol of integra

S m(dv)=S -9.8m(dt)+S kv(dt)

vm=-9.8mt+kvt

v(m-kt)=-9.8mt=>

v is a function of t=> v(t)=(-9.8mt)/(m-kt)

I think the answer is "neither"

- Anonymous1 decade ago
Please put this in standard notaion....NO one, including myself, knows what the HECK you are talking about..