Setting a function equal to an integral

Question

I am trying to solve for the constant of integration in simple calculus problems.

v[t_] := Integrate[-0.08 t, t] + C
v[t]

gives me

C - 0.04 t^2

Which is good, but then when I try

Solve[v[0] == 8]

It gives me an error because Im trying to integrate with respect to zero, because my function changes that.

I assume there is something really simple that I'm missing on how to make this work.

Answer 1

Use an immediate assignment to define v:

v[t_] = Integrate[-0.08 t, t] + c
(*    c - 0.04 t^2    *)

Solve[v[0] == 8]
(*    {{c -> 8.}}    *)

Here's a tutorial on the distinction between immediate and delayed assignments.

Alternatively, use a definite integral:

t0 = 0;
v0 = 8;
v[t_] = v0 + Integrate[-0.08 s, {s, t0, t}]
(*    8 - 0.04 t^2    *)