Find the law according to which the mass of the rocket varies with time, when the rocket moves with a constant acceleration w, the external forces are absent, the gas escapes with a constant velocity u relative to the rocket, and its mass at the initial moment equals `m_0`.

Explanation

According to the question, `vecF` (external force) =0
So, `m(dvecv)/(dt)=(dm)/(dt)vecu`
As `dvecvuarrdarrvecu`,
so, in scalar form, `mdv=-udm`
or, `(wdt)/(u)=-(dm)/(m)`
Integrating within the limits for `m(t)`
`(wt)/(u)=-underset(m_0)overset(m)int(dm)/(m)` or, `v/u=-1n(m)/(m_0)`
Hence, `m=m_0e^(-(wt//u))`