# How to Find Jerk from Discrete Velocity Data?

I have measured the velocity of an object at discrete intervals. I want to find the corresponding acceleration and jerk of the object. How do I do this with discrete values rather than continuous variables?

I think acceleration is simply a = (V2-V1)/(t2-t1), but what times do I use for the jerk equation?

If I were to plot these values, what times would I plot acceleration and jerk against? i.e. does a1 pair with t1 or t2? Or do I plot a1 over the interval between t1 and t2? Since what you calculated here is not instantaneous acceleration but rather average acceleration, you can't determine the average jerk. You can only estimate a value for average jerk. And because it is only an estimation you can consider the average accelerations you obtained between $$t_1$$ and $$t_2$$ to be instantaneous acceleration at $$(t_1+t_2)/2$$ just for the sake of finding an estimate. Note: This won't give you the exact value of jerk but only an estimate.