Posted by sreeram on .
find mass of a rocket as a function of time,if it moves with constant acceleration a in absence of external forces.the gas escapes with a constant velocity u relative to the rocket and its mass initialy was m'
The rate of mass release, and the thrust F, would have to vary continuously to maintain a constant acceleration. That is not the way rockets usually work, but it is possible.
a = F(t)/m(t)= (u *dm/dt)/m
Integrate and solve the differentuial equation with m = m' at t = 0
u ln (m'/m) = a*t
(a/u)t = ln(m'/m)
e^(at/u) = m'/m
m = m'*e^(-at/u)