A motorbike starts from rest with an acceleration of 2.5 m/s², just as a truck passes it at a…

Step 1. Catching up. $1.25\ \text{m/s}^2 \times t^2 = 12\ \text{m/s} \times t$, so $t = \dfrac{12\ \text{m/s}}{1.25\ \text{m/s}^2} = 9.6\ \text{s}$.

Step 2. Distance. $12\ \text{m/s} \times 9.6\ \text{s} = 115.2\ \text{m}$.

Step 3. The widest gap. Equal velocities: $2.5\ \text{m/s}^2\,t = 12\ \text{m/s}$, at $t = 4.8\ \text{s}$. Truck: $57.6\ \text{m}$; motorbike: $\tfrac12 (2.5)(4.8^2) = 28.8\ \text{m}$. Gap: $28.8\ \text{m}$.