A bus joins a highway along a straight slip road…

Step 1. Acceleration. $a = \dfrac{v^2 - u^2}{2s} = \dfrac{(18\ \text{m/s})^2 - (8\ \text{m/s})^2}{2 \times 130\ \text{m}} = 1.0\ \text{m/s}^2$.

Step 2. Time. $t = \dfrac{v - u}{a} = \dfrac{10}{1.0} = 10\ \text{s}$.