Derive Equation for Velocity as Function of Time - Help Integrating

[Punkyc7]

Homework Statement

Derive an equation for an objects velocity as a function of time

Homework Equations

i have that a=-(kvo/m)

The Attempt at a Solution

so i get dv/v=-(k/m)dt then i get
1/v= -kt/m +C and then I am stuck

 

[XanziBar]

It's been awhile, but I think the integral of dv/v is the natural log of v. Then you can probably exponentiate both sides

 

[Punkyc7]

so
lnv= ln(-kt/m +C)
then
e^lnv=e^ln(-kt/m +C)
so is this right
v=e^ln(-kt/m +C)

 

[XanziBar]

you only have the 1/v on the left side:

lnv= (-kt/m +C)

e^lnv=e^(-kt/m +C)
so is this right
v=e^(-kt/m +C)

yeah, that seems about right. I'm a little worried about the units, maybe you can do something with that k or C...

 

[rl.bhat]

a=-(kvo/m)
The above relation represent rocket equation where vo represents the velocity of escaping of gas which is constant an k represents dm/dt, the mass of fuel ejected per unit time. It is also constant. Here mass of the fuel is varying with time.
So you can find the velocity of the object with respect to mass rather than the time.
a = dv/dt = - (dm/dt)vo/m
dv = -vo(dm/m). To find the velocity take the integration between the limits m = Mo to m = M.