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

• Mar 22nd 2013, 10:08 AM
calltronics
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..........
$S_a = (V_m^2 - U_1^2)/(2*A_a)$

And obviously
$S_d = (V_2^2 - V_m^2)/(2*A_d)$

So if acceleration distance $S_a = S_t - S_d$

Then we can substitute Sa in above to get: - $S_t - S_d = (V_m^2 - U_1^2)/(2*A_a)$
So
$S_d = S_t + (V_m^2 - U_1^2)/(2*A_a)$

Combining gives us
$S_d = (V_2^2 - V_m^2)/(2*A_d) = S_t + (V_m^2 - U_1^2)/(2*A_a)$

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
• Mar 22nd 2013, 01:36 PM
Shakarri
Re: Is this equation Correct and can it be simplified/ solved for Vmax
This line
Quote:

Originally Posted by calltronics
So
$S_d = S_t + (V_m^2 - U_1^2)/(2*A_a)$

Should be
$S_d = S_t - (V_m^2 - U_1^2)/(2*A_a)$

That's all
• Mar 22nd 2013, 02:11 PM
calltronics
Re: Is this equation Correct and can it be simplified/ solved for Vmax
you sure?
• Mar 23rd 2013, 03:24 AM
Shakarri
Re: Is this equation Correct and can it be simplified/ solved for Vmax
$S_a=S_t-S_d$

So
$S_d=S_t-S_a$

$S_d = S_t - (V_m^2 - U_1^2)/(2*A_a)$
• Mar 23rd 2013, 03:34 AM
calltronics
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!
• Mar 23rd 2013, 03:50 AM
calltronics
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

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