How to calculate acceleration from discrete samples of velocity? I have a device that I made which is able to calculate distance moved and can determine time.
I take samples of time every x distance. Giving me n velocity samples.
I currently show the user 2 values : max velocity and avg velocity.
What I need help with can be broken down into 2 questions:


*

*How can I calculate acceleration from this data?

*What would be the most useful value to show? Avg acceleration? Peak?


So you have context to answer this question, the device measures the speed at which athletes are lifting a barbell.
 A: A fairly simple way of treating the data is to present them as a histogram:

Each data point (here 5 data points) is the quotient of the distance moved in that interval, say $\Delta y$, by the time interval $\Delta t$ and is the average velocity during that time interval:
$$v_i=\frac{\Delta y_i}{\Delta t_i}$$
Where $i$ indicates interval number $i$.
For simplicity's sake, I'll assume all $\Delta t_i$ to be of the same value (but that's not strictly speaking necessary).
That would allow also to calculate the average acceleration $a$ at the end of each time interval, here represented by the green line, because:
$$a_i=\frac{v_i-v_{i-1}}{\Delta t_i}$$
That would give a rough idea of how $a$ evolves over time, as well as peak $a$ values.
If the time intervalls $\Delta t_i$ are sufficiently small, then the obtained values for $v$ and $a$ will tend to the true values (as opposed to averages).
A: I think you should take the sample velocities and divide them by the respective times after minusing the previous velocities to obtain the accelerations. If the time interval between calculating the discrete sample velocities are too small, then the above-got values may be taken as instantaneous acceleration. Now plot these over graph wrt time. Now here we can obtain the maxima and minima.
Now if we sum up all the velocities and divide this with the sum of the times, we get the average acceleration. 
In this case, either the maximum acceleration or the instantaneous acceleration should be taken into account if the time-gaps are small enough.
