Speed of a Body on a Smooth Surface over Time

[Bitupon]

Question:A body of mass is placed on a smooth horizontal surface. The mass of the body is decreased exponentially with disintegration constant λ. Assuming that the mass is ejected backwards with a relative velocity u.If initially the body
was at rest, the speed of the body at time t is:
(a)ue^(-t)
(b)uλt
(c)ue^(-λt)
(d)u{1-e^(-λt)}.

 

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[OlderDan]

I guess this does not qualify as speedy, but do you know the rocket equation? What you have is a rocket. Figuring out the speed of a rocket is not trivial, but it all depends on conservation of momentum. A decent explanation is given here.

http://ed-thelen.org/rocket-eq.html

The final equation can be written as

v(t) = v_0 + uln \left[ \frac{M_0}{M(t)} \right]

In your problem, the initial velocity is zero. If you understand logs and exponentials, you can do the rest.