Good day to you all,

I have the following fixed values: -Acceleration = 1000 mm/sTime is totally variable/infinite and not a factor^{2 }- (A_{a})

Deceleration = -400 mm/s^{2 }- (A_{d})

Total Distance = 450 mm - (S_{t})

The object starts from velocity(u_{1)}and accelerates a distance (S_{a})to reach a velocity of V_{m. }It then decelerates from velocity V_{m}a distance (S_{d})to final velocity (V_{2}).

Distance S_{a}and S_{d}have to total the full distance travelled - S_{t }

I would like to know the maximum velocity reached by the object.

From this I can the easily calculate the distance S_{a}and S_{d. }

Now I believe that..........

And obviously

So if acceleration distance

Then we can substitute S_{a }in above to get: -

So

Combining gives us

I have tried multiply out and simplifying and in all honesty disappeared up .......

If I am right on the track, and that would be great!

Can one of you gurus simplify it and solve for V_{m}for two states: -

- Values of starting velocity U
_{1}and finishing velocity V_{2 }both are 0- Given any starting velocity U
_{1}and finishing velocity V_{2 }if that's possible

Thank you so much