1. The problem statement, all variables and given/known data 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 2. Relevant equations accel=v*dv/ds=dv/dt=a 3. 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.