Good day to you all,
I have the following fixed values: -Acceleration = 1000 mm/s^{2 }- (A_{a})Time is totally variable/infinite and not a factor
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