Good day to you all,

I have the following fixed values: -Acceleration = 1000 mm/s^{2 }- (A_{a})

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

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

Time is totally variable/infinite and not a factor

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..........

$\displaystyle S_a = (V_m^2 - U_1^2)/(2*A_a)$

And obviously

$\displaystyle S_d = (V_2^2 - V_m^2)/(2*A_d)$

So if acceleration distance $\displaystyle S_a = S_t - S_d$

Then we can substitute S_{a }in above to get: -$\displaystyle S_t - S_d = (V_m^2 - U_1^2)/(2*A_a)$

So

$\displaystyle S_d = S_t + (V_m^2 - U_1^2)/(2*A_a)$

Combining gives us

$\displaystyle S_d = (V_2^2 - V_m^2)/(2*A_d) = S_t + (V_m^2 - U_1^2)/(2*A_a)$

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