- #1
tungle
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"Strange" case in finding acceleration
Hello there, looks like a fantastic forum here. I got a problem popped up during my work, hope you can help me out.
I have a car:
- at a distance D away from destination
- current velocity V0
- time to go t : the time period I want the car to spend until reaching destination
I discretize time into seconds. At every every second, I want to find suitable acceleration (or deceleration) so that it can arrive at destination at t.
I apply this equation
D = V0 t + (1/2)at^2
(Given the equation is applied for constant-change in velocity, reapplying it every second yields some error, but it's minor thing)
I came up with something strange:
If t is sufficiently small, then the car arrives exactly at t once. (case 1)
If I set t too high, the car arrives at the destination early (much less than t), go past destination for some time, then go backwards
to reach destination at given t. (case 2)
My question: is there any constraint for t to always yield case 1, preventing case 2 happening.
To be specific, I put an example in the spreadsheet here:
https://spreadsheets.google.com/spr...TGYzRHB1V1RWVjc3ZEE&hl=en_US&authkey=CIyymf8E
Table 2 is where the case 2 happened. Round-up error is ignored.
Thanks much
Hello there, looks like a fantastic forum here. I got a problem popped up during my work, hope you can help me out.
I have a car:
- at a distance D away from destination
- current velocity V0
- time to go t : the time period I want the car to spend until reaching destination
I discretize time into seconds. At every every second, I want to find suitable acceleration (or deceleration) so that it can arrive at destination at t.
I apply this equation
D = V0 t + (1/2)at^2
(Given the equation is applied for constant-change in velocity, reapplying it every second yields some error, but it's minor thing)
I came up with something strange:
If t is sufficiently small, then the car arrives exactly at t once. (case 1)
If I set t too high, the car arrives at the destination early (much less than t), go past destination for some time, then go backwards
to reach destination at given t. (case 2)
My question: is there any constraint for t to always yield case 1, preventing case 2 happening.
To be specific, I put an example in the spreadsheet here:
https://spreadsheets.google.com/spr...TGYzRHB1V1RWVjc3ZEE&hl=en_US&authkey=CIyymf8E
Table 2 is where the case 2 happened. Round-up error is ignored.
Thanks much