So, one way would be to arrange the data in long format
id trial velo intens
1 1 0.3 0.4
1 2 0.2 0.3
1 3 0.1 0.2
1 4 0.4 0.2
#Edited to add: you'd have to choose some slice of time
and average the velocity and intensity within that time
(for each participant and within each trial) to get your
data into a "modellable" numeric form.
Maybe you can average over the whole minute,
maybe you want to use 10 second slices, maybe 1 second slices -
what's reasonable depends of subject knowledge and other data properties.
And run a multilevel regression analysis, e.g. in R lmer like this
model<-lmer(velo ~ (1|id) + intens, data=data) #though you'd probably need to person-mean center intensity and use this centered variable as predictor
#in this approach you could also include a random intercept of trial (1|trial) if you feel trials are meaningfully different from each other
From this analysis you'd get an average estimate about the relationship between velocity and intensity for each participant, as well as a global estimate of this relationship across all participants. See lmer and general multilevel regression tutorials (there are tons online) to get a better idea of this approach.
Another way would be to use repeated measures correlations. E.g. in R
rmcorr(participant=id, velo, intens, dataset=data)
Which gives you the average within-participant correlation between velocity and intensity. See this article for reference.
Yet another way might be to calculate a correlation for each participant, Fisher-transform these correlations, average the transformed correlations, and then back-transform the average (see, e.g. this article, but I'm not sure what's the status of that practice nowadays.
So, first thing for you to do is to get the data into a numeric and data frame format. Choose a time slice over which you average the values or use the raw values from the 0.125 second clips depending on which is reasonable based on your subject knowledge. Though if you use raw values you will have an enormous dataset of about 14 400 rows per participant, which may not be necessary and may require a lot of computational power to analyze.
At least in softwares I'm familiar with, regardless of your analytical approach, you'd organize your data like this:
ID trial velocity intensity
1 1 100 120
1 1 110 110
20 30 120 130
20 30 110 140
So, each participant gets as many rows as there are trials * time slices within a trial. In other words, each row corresponds to a particular time slice for each participant within each trial. If you choose to average over the whole trial, you'd have 30 rows per participant.
Then, you can use any of the approaches I suggested on the data. You should probably read some background on each approach to decide which works for you.