# Constant acceleration and free fall

Hey, I've been having some problems with finding out the rocket's maximum altitude and was wondering if anyone could help. The question information is:

A 200kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 34.0 for 31.0 , then runs out of fuel. Ignore any air resistance effects.

So far i've taken:

sf= si + 0.5(34.0m/s2)(31.0s)^2 and I got 16337 m however, i know that this is only from 0m to the point at which the rocket runs out of fuel.

Next, I was trying to find the distance from this point to the point where the rocket will reach a final velocity of 0m/s however I'm unsure how to do this. I know that the acceleration now will be -9.81m/s2 but i'm unsure how to complete this problem.

Thanks a lot!!