Maximum Velocity of a Boat in a Race

[beatlemaniac]

Homework Statement

A boat starts a race at 3 m/s, accelerates uniformly for 10 seconds, then travels with constant velocity for 6 seconds. It then slows uniformly to rest in another 6 seconds. If the boat has traveled a total distance of 225m, find the maximum velocity.

Homework Equations

a(t) = v`(t) = s``(t)

The Attempt at a Solution

Obviously the boat has three phases of motion:
- the initial acceleration
- the constant velocity
- and the negative acceleration until it comes to rest

And I need to find the constant velocity. However I am honestly stuck I do not even know how to approach this question! Please help!

 

[nasu]

The analysis is OK.
Now you need to write the equations of motion for each one of the three phases.
Add the expressions for the three distances and this will be 225 m.
Solve the equation to find the speed.