How far does the train travel before the engine is ....

[siimplyabi]

Homework Statement

.[/B]
A model steam train engine has a mass of 2.3 kg is powered by a sterno and white gas mixture that heats a small boiler. Once sufficient steam pressure is produced, the train is released from rest. The train travels along a straight and level track. At any time after release and before it comes to rest, the train’s speed can be expressed by v = 5t + 2t 2 − t 3 .

a) How far does the train travel before the engine is producing maximum force?

Homework Equations

The Attempt at a Solution

I've only been thinking on how i can approach this problem and I haven't had any luck. I've tried drawing Free body Diagrams and drawing forces but it's not helping and its because i don't really understand what they are asking for.

Am I looking for a displacement? Now i know the initial position is 0 since it was released from rest.
Now I am guessing max force is the force needed to get the train moving?
Please help.

 

[siimplyabi]

The v= 5t+2t^2-t^3

 

[Mister T]

Now i know the initial position is 0 since it was released from rest.

Released from rest means the initial velocity is zero.

Now I am guessing max force is the force needed to get the train moving?

When the force has its maximum value, what can you say about the acceleration?