When is this voltage source activated?
\$u(t)\$ is the Unit Step Function. More than a mathematical function is a tool that allows us to model activations and deactivations in electrical circuits and abrupt changes of state in general. This function is defined as

$$
u(t) = \left\lbrace
\begin{matrix}
0 \qquad t&lt;0 \\
1 \qquad t&gt;0
\end{matrix}
\right.
$$

For your question, the variable \$t\$ has been transformed by a reflection with respect to \$t = 0\$. This means that

$$
u(-t) = \left\lbrace
\begin{matrix}
0 \qquad t &gt; 0 \\
1 \qquad t &lt; 0
\end{matrix}
\right.
$$

What does this mean? It means that the power supply has been active from \$t = -\infty\$ to \$t = 0\$, when it was deactivated. In other words, this source should only be taken into account in determining the initial conditions in the analysis of the circuit.