Acceleration and jerk calculations

[SlowGoing]

I’m trying to calculate the theoretical jerk and acceleration curve/distance/time for an elevator.

I have the constant starting jerk set to 1m/s3, constant acceleration set to 1m/s2 and full speed set to 1m/s.
Looking at Wikipedia about both, I can work out the figures about acceleration but I get stuck with the jerk.

Assume starting velocity is 0.
Assume jerk at start and at end of acceleration – S curve type of thing.

So I would like to know how to calculate:

Time and distance traveled during the starting jerk
Time and distance traveled during the acceleration
Time and distance traveled during the jerk at the end of the acceleration curve
Time and distance traveled by the time I reach full speed, which should just be an addition of the above.

I hope the above makes sense.
Thanks

 

[andrewkirk]

The first thing to work out is for how long the jerk goes that increases the acceleration from $0ms^{-2}$ to $1ms^{-2}$ and how long the reverse jerk goes that reduces the acceleration back to 0.

Next, calculate the total change in velocity and distance traveled during those two phases.

To get change in acceleration (velocity) over a time period we need to integrate the jerk (acceleration) over that period. So the acceleration (velocity) at a point in time within a period will be the acceleration (velocity) at the beginning of the period plus that integral.

To get distance traveled over a period, we integrate velocity over that period.

 

[SlowGoing]

I properly did not explain myself very well.
How do I calculate the jerk distance/time with the figures above ?

Thanks

 

[andrewkirk]

Jerk is the time rate of change in acceleration. You have said the jerk is $1ms^{-3}$, which means it increases the acceleration by $1ms^{-2}$ every second. Given that, how long does it take to increase the acceleration from $0ms^{-2}$to $1ms^{-2}$?