2. Given the function $f(x)=\left\{\begin{array}{ll}(2 a-1) x+3 a-4, & x \leqslant t \\ x^{3}-x,\end{array}\right.$, regardless of the value of $t$, the function $f(x)$ is always non-monotonic on the interval $(-\infty,+\infty)$. Then the range of values for $a$ is $\qquad$.
2. $a \leqslant \frac{1}{2}$ Detailed explanation: If $2a-1>0$, the linear function is monotonically increasing, and when $t$ is sufficiently large, the function $f(x)$ will definitely be monotonically increasing.
If $2a-1<0$, the linear function is monotonically decreasing. However, the cubic function will eventually be monotonically increasing at some point. Therefore, there is no monotonicity. If $2a-1=0$, the linear function has no monotonicity. $\quad \therefore 2a-1 \leqslant 0 \Rightarrow a \leqslant \frac{1}{2}$.