recursion - How can I express this recurrence function in Mathematica?

\begin{equation} r_{i+1}=r_{i}+V_{i}{\Delta}t \end{equation}

Where \begin{equation} V_{i}=(0.01, 0.40) \end{equation} and ${\Delta}t$ is the difference in time.

My implementation (this is for ${\Delta}t$ = 1):

V = {0.01, 0.4};
list = List[Do[Print[V*t], {t, 1, 10}]];

* $RecursionLimit::reclim: Recursion depth of 1024 exceeded. *

This generates the correct values but I can't change ${\Delta}t$ and the values aren't stored as a list (for use with ListPlot[...]).

I have tried other implementations such as r[t_]=r[t]+V*t and r[t_+1]=r[t]+V*t but this didn't work.

Answer

With

v = {0.01, 0.4};

you can define

r[n_, dt_] := r[n, dt] = r[n - 1, dt] + v dt
r[0, dt_] = {0, 0}

Now

Table[r[n, 1], {n, 1, 10}]

{{0.01, 0.4}, {0.02, 0.8}, {0.03, 1.2}, {0.04, 1.6}, {0.05, 2.}, {0.06, 2.4}, {0.07, 2.8}, 
 {0.08, 3.2}, {0.09, 3.6}, {0.1, 4.}}

and

Manipulate[
 ListPlot[Table[r[n, deltat], {n, 1, 10}], PlotRange -> 20],
 {{deltat, 1, "Δt"}, 0, 5}]

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