1. The problem involves understanding the given time intervals $\Delta t$ and average forces $F_{av}$. 2. We are given four time intervals: $\Delta t = 0.24$ s, $0.12$ s, $0.48$ s, and $0.36$ s. 3. We are also given two average forces: $F_{av} = 4.2 \times 10^{5}$ N and $5.4 \times 10^{5}$ N. 4. Typically, in physics, the impulse-momentum theorem relates force and time interval as $F_{av} \Delta t = \Delta p$, where $\Delta p$ is the change in momentum. 5. Without additional context or a specific question, we can interpret these values as options or data points for a problem involving impulse or force over time. 6. If the question is to identify or compare these values, note that the product $F_{av} \Delta t$ gives the impulse. 7. For example, for $F_{av} = 4.2 \times 10^{5}$ N and $\Delta t = 0.24$ s, impulse is $4.2 \times 10^{5} \times 0.24 = 1.008 \times 10^{5}$ Ns. 8. Similarly, for $F_{av} = 5.4 \times 10^{5}$ N and $\Delta t = 0.12$ s, impulse is $5.4 \times 10^{5} \times 0.12 = 6.48 \times 10^{4}$ Ns. 9. These calculations help understand the effect of force applied over different time intervals. 10. To solve any specific question, please provide the exact problem statement or what is asked regarding these values.