How to integrate part of a function over specified timestep

For a project I have to get a value for F_a at every time interval and then use that value to calculate v_veh, w_w, slip, Cf and lastly a new value for F_a to use in next iteration.

For parts of v_veh and w_w, I have to integrate over the timestep to get a value to use for the next calculation.

Below is my code so far, I have tried to implement cumtrapz to do this integration for me, but I have not been successful.

%Constants
m = 5           %[kg]
r = 0.02            %[m]
g = 9.81
Tm = m*g*0.2
N = m*g
F_rr = 0.03
F_res = m*g*F_rr
%Wheel moment calculation
spokes = 8
L_s = 0.02      %length of spokes[m]
m_s = 0.01      %mass per spoke[kg]
m_r = 0.1       %mass of rim[kg]
I_w = spokes*((1/3)*m_s*L_s^2)+(m_r*L_s^2)

%Constant Coefficients
B = 10
C = 1.9
D = 1
E = 0.97

%Create loop

t = 0:1:20
N = length(t)

v_veh= NaN(1,length(t));        %empty vehicle velocity vector
w_w= NaN(1,length(t));          %empty wheel velocity vector
slip = NaN(1,length(t));        %empty slip vector
CF =NaN(1,length(t));           %empty friction coefficient vector



v_veh(1) = 0
w_w(1) = r*((1/I_w)*(Tm*t(1)))
slip(1) = 1
CF(1) = D*sin(C*atan(B*slip(1)-E*(B*slip(1)-atan(B*slip(1)))))
F_a(1) = CF(1)*N

for i = 2:1:20
    v_veh(i) = (1/m)*cumtrapz(F_a(i-1)-F_res)
    w_w(i) = ((1/I_w)*cumtrapz(Tm-r*F_a(i-1)))
    slip(i) = (r*w_w(i)-v_veh(i))/(r*w_w(i))
    CF(i) = D*sin(C*atan(B*slip(i)-E*(B*slip(i)-atan(B*slip(i)))))
    F_a(i+1) = CF(i)*N
end
figure(1)
plot(t,v_veh,'r',t,r*w_w,'b')
figure(2)
plot(t,F_a)

Any help would be greatly appreciated

[Walter Roberson]

    v_veh(i) = (1/m)*cumtrapz(F_a(i-1)-F_res)

F_a(i-1) is a scalar. F_res is a scalar. scalar minus scalar is scalar. So you are asking to cumtrapz() a scalar. trapz() applied to a scalar is always 0 -- a single point has no width.

[Charles Steyn]

Thank you. I will continue working on my code.