How to integrate an implicit acceleration function to a fitting pair of graphs of velocity and displacement

Hello!

New to matlab, so sorry if the question appears a bit of dumb

Im currently trying to plot the displacement of a falling pellet which acceleration follows implicit function f = @(t,a) exp((4.33254*w)/(9.81-a) - t/0.1036881 - 0.418/(0.00032*v)) - ((0.013864*v*w)/((9.81-a)*(0.418+0.00032*v)) - (0.00032*v)/(0.418+0.00032*w))

Where v and w are parameters to be adjusted.

The goal here is to first calculate the integral of the function to obtain a velocity function where the initial velocity is equal to 0 when t=0 and then obtain the integral of the velocity function to calculate the displacememt, where x=h (yet another parameter) when t=0 as well

However I struggle to find the correct sets of tools for that

Any advice is appreciated!

The deceleration graph looks somewhat like this btw

Answer 1

[Alan Stevens]

Look up ode45 for the integration (for a fixed set of parameters) and fminsearch for fitting the parameters to known data.