"Euler method to solve first order differential equation for 1D free fall,dy/dt = v_y"

"f[t] plays the role of y[t] "
"G[t] plays the role of vy[t] "

(*initialisation*)
g=9.81;
tfinal=10;tinit=0;Nstep=1000;
f0=0;(*initial value of f[t]*)
vy0=0;

(*define G[t]*)
G[i_]:=-g*t[i]+vy0;
(*end of 
initialisation*)


(*definitions*)
Deltat=(tfinal-tinit)/Nstep;
ilast=Nstep+1;
f[0]=f0;
(*end of definitions*)

t[i_]:=tinit+i*Deltat;
For[i=0,i≤ilast-1,i++,
f[i+1]=f[i]+G[i]Deltat;
];
ttf=Table[{t[i],f[i]},{i,0,ilast-1}];
lptttf=ListPlot[ttf,PlotLabel->"f(t) vs. t",PlotRange->All];

ftheory[t_]:=-g*t^2/2+f0;
plt=Plot[ftheory[t],{t,tinit,tfinal},PlotRange->All,PlotStyle->Red];
Show[lptttf,plt]