How to identify negative slope from plot data?

So I'm trying to do some lap simulation work and I want to isolate the braking zones (negative slope) from a velocity vs. time data plot. I was thinking I could get it to identify mins/maxs but I would still need to identify if the region is sloped downward. How can I get the program to recognize that?

Answer 1

[KSSV]

t = linspace(0,2*pi) ;
y = sin(t) ; 

m = [0 diff(y)./diff(t)] ; 

plot(t,y) ;
hold on
plot(t(m<0),y(m<0),'+r')
plot(t(m>=0),y(m>=0),'+g')

legend('sine','negative slope','positive slope')

Answer 2

[Sam Chak]

Hi @Michael Tognotti

This is just a basic idea for identifying the region of negative slope. Generally, the numerical differentiation of the velocity data is obtained.

t  = linspace(0, 180, 1801);
V  = sin(2*pi/180*t);               % velocity data
dV = gradient(V, t)/(2*pi/180);     % numerical differentiation of V: cos(2*pi/180*t)
plot(t, [V' dV'], 'linewidth', 1.5), grid on, 
ylim([-1.5 1.5]), yline(0, '--')
xlabel('t'), legend('V', 'dV', '')
xtval = 0:15:180; xticks(xtval)

idx = find(dV < 0);
slopeStart = t(idx(1))

slopeStart = 45.1000

slopeEnd = t(idx(end))

slopeEnd = 134.9000

The region of negative slope lies between and .