use of matlab in physics

You have a force from many forces that is

F=F+Fc-Fv-D

where

F=400 N
Fc=488*exp(-(t/0.67)^2)  N
Fv=25.8v
D=0.34911(1-0.25*exp(-(t/0.67)^2)*v^2

i was asked to use eulers method to calculate in matlab the position of a runner who is moving with these forces (F is moving forward motion, Fc is extra motion forward when body is leaned and back is curled, Fv is a force that prevents F to continue to infinity and decreases acceleration as function of v of runner and D is airdrag)

here is what i wrote but without clearly getting a right answer:

vl=[];

x=[];

t=[];

a=[];

vl(1)=0;

n=2;

x(1)=0;

t(1)=0;

dt=0.05;

while x(n-1)<100

      F=5;

      Fc=6.1*exp(-(t(n-1)/0.67)^2);

      Fv=25.8*vl(n-1);

      D=0.34911*(1-0.25*exp(-(t(n-1)/0.67)^2))*(vl(n-1))^2;

      a(n-1)=F+Fc-Fv-D

vl(n)=vl(n-1)+a(n-1)*dt;

x(n)=x(n-1)+vl(n)*dt;

t(n)=t(n-1)+dt;

n=n+1;

end

   plot(t,vl,'r');

hold on

plot(t,x,'g');

legend('vl','x');

Answer 1

[the cyclist]

I notice two things:

1. You run your while loop out to x=100 or so, but with the constants you have, all the interesting action is taking place at x<1. Temporarily, you might consider changing the limit to x(n-1)<1, while you debug.
2. You divided two of your force constants (F and Fc) by a factor of 80, but you did not do the same with the other two (Fv and D). I did not look in detail (something with units, which you did not specify?), but that might lead to the current incorrect behavior, where the runner reaches top velocity in about a second.

I suggest you write out your equations with the units included, to ensure that the units all match.

There are also some significant MATLAB-specific improvements that could be made to your code, but I think you should focus on getting the physics/math correct first.