Rocket ascending with acceleration then coasting to maximum altitude

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cheerspens
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Homework Statement


A rocket is fired vertically and ascends with a constant vertical acceleration of 20.0 m/s^2 for 2.00 seconds. Its fuel is then used up and it continues as a free object. What is the maximum altitude reached?

Homework Equations


X=Xo+volt+(1/2)at^2
V=Vo+at
2a(X-Xo)=V^2-Vo^2

The Attempt at a Solution


I don't know how to solve for the point at which the rocket runs out of fuel. Once I can do that I think I will be able to find the maximum altitude reached as it asks in the problem.
 

Discussion

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They tell you at what time the rocket runs out of fuel. Use this to determine the height and velocity that the rocket is at when the fuel runs out.