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## 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.