How can I convert a speed profile to displacement graph

I have a speed graph that looks like the image below. The y-axis is in (m/s) and the x-axis is in (s). To generate the plot below i made use of 3 equations and applied the fplot function

max_spd = 4;
a = 2/3; %acceleration 

fplot(@(x) (a)*x,[0 6],'g')
fplot(@(y) max_spd,[6 13.75],'g');
fplot(@(x) -(a)*x + (19.75)*(a),[13.75 19.75],'g')

How can I convert this velocity-time plot to a displacement-time graph?

so far I have this,

max_spd = 4;
a = 2/3; %acceleration
fplot(@(x) 0.5*(a*x)*x,[0 6],'k');
fplot(@(x) 4*x-(0.5*4*6),[6 13.75],'k');
fplot(@(x) 0.5*(-a)*x*x+(19.75)*a*x - (4*7.75) - (0.5*6*4),[13.75 19.75],'k');

which gives me this plot, is there a better function that will allow me to plot the displacement-time plot? Or is there a better method to perform this conversion?

Answer 1

[Walter Roberson]

Don't use 3 functions.

max_spd = 4;
a = 2/3; %acceleration 
fun = @(x) (0 <= x & x < 6) .* (a) .* x + ...
           (6 <= x & x < 13.75) .* max_spd.*ones(size(x)) + ...
           (13.75 <= x & x < 19.75) .* a .* (19.75-x);
fplot(fun, [0 20]); ylim([0 5])

Now you can process the single function that gives the speed into displacement, by integrating . Chances are that you will want cumulative output, so use something like cumtrapz()