Integration (displacement or position)

[kieran1black2]

Homework Statement

the trouble is in the integration on the left side (go straight o my answer down the bottom of the page)... please help me...

mg-u-kv=m*a

where (all constant)
m= mass= 3000
g=gravity=10
u=thrust=172000
k=30

v=velocity=variable
a=acceleration=variable

Homework Equations

accel=v*dv/ds=dv/dt=a

The Attempt at a Solution

30000-172000-30v = 3000*v*dv/ds
-142000-30v = 3000*v*dv/ds
-(142000+30v) = 3000*v*dv/ds
142000+30v = -3000*v*dv/ds
(142000+30v)/v*dv = -3000*ds
v/(142000+30v)*dv = -1/3000*ds

and then integrate both sides, this is where my calculus stops

i know the right side (-1/3000*ds) becomes -1/3000s + c
where
s= displacement or position and
c= constant
i have 2 scenarios

when s=0, v=1000
and what i need to find is when v=0 what is s?


so once i integrate the left side i sub those values in.

 

[Delta]

(142000+30v)/v*dv = -3000*ds
v/(142000+30v)*dv = -1/3000*ds

Are you sure about this transition?

 

[kieran1black2]

if you think you can do it without that transition... go for it... that's just how i interpreted the question