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.
Best Answer
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).