Finding max height and speed before it hits the ground of a rocket

[llach]

Homework Statement

A model rocket initially at rest on the ground is fired vertically upward, and the engine thrust produces a constant acceleration a = 40 m/s2. After running for 2.5 s the engine is cut off and then the rocket is in free fall. (a) Find the maximum height that the rocket reaches. (b) Find the speed of the rocket just before it hits the ground.
Ans: (b) 635 m (c) 112 m/s
Note: The rocket travels with 40 m/s2 acceleration during the first 2.5 s (gravity effect included).

Homework Equations

The Attempt at a Solution

 

[rl.bhat]

In the relevant equations, can you write the kinematic equations. And using the given data, you can select a proper equation to solve the problem.