# Thread: Is this equation Correct and can it be simplified/ solved for Vmax

1. ## Is this equation Correct and can it be simplified/ solved for Vmax

Good day to you all,

I have the following fixed values: -
Acceleration = 1000 mm/s2 - (Aa)
Deceleration = -400 mm/s2 - (Ad)
Total Distance = 450 mm - (St)
Time is totally variable/infinite and not a factor

The object starts from velocity(u1) and accelerates a distance (Sa)to reach a velocity of Vm.
It then decelerates from velocity Vm a distance (Sd)to final velocity (V2).
Distance Sa and Sd have to total the full distance travelled - St

I would like to know the maximum velocity reached by the object.
From this I can the easily calculate the distance Sa and Sd.

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 Sa 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 Vm for two states: -

1. Values of starting velocity U1 and finishing velocity V2 both are 0
2. Given any starting velocity U1 and finishing velocity V2 if that's possible

Thank you so much

2. ## Re: Is this equation Correct and can it be simplified/ solved for Vmax

This line
Originally Posted by calltronics
So
$\displaystyle S_d = S_t + (V_m^2 - U_1^2)/(2*A_a)$
Should be
$\displaystyle S_d = S_t - (V_m^2 - U_1^2)/(2*A_a)$

That's all

you sure?

4. ## Re: Is this equation Correct and can it be simplified/ solved for Vmax

$\displaystyle S_a=S_t-S_d$

So
$\displaystyle S_d=S_t-S_a$

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

5. ## Re: Is this equation Correct and can it be simplified/ solved for Vmax

Dam, never doubted you!
That is why it never calculate out properly!

6. ## Re: Is this equation Correct and can it be simplified/ solved for Vmax

So the question now is........
Can anyone rearrange this lot to solve Vm

1. When V2 and U1 = 0
2. Arbitrary values of V2 and U1

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