In MATLAB for a vector the index start from 'one'(1) not 'zero'(0).
supposeif you have a vector v=[2,4,6,3,9,7]
you can axcess thosevalues as v(1) and it will return 2,
v(2) will return 4
v(3) will return 6 and so on.
if you try to axcess v(0) it will return an error, because there is no such element with 'zero;(0) as index. so try to avoid the occurence of v(0) term in your loop.
I am re writing your program, i have understood the exact location of your problem but i havent got the value of A from your program, so i am taking A=4 an writing it.
clc
clear all
v0=0 % initial temperature
t0=0 % initial time
A=2
x=0:0.1:5
n=length(x)
t=x;
v=zeros(1,n);
v(1)=v0+A*(t(1)-t0)
for k=2:n
v(k)=v(k-1)+A*(t(k)-t(k-1));
end
