Given the functions describing the distance of cars A and B from the starting point as functions of time $t$:

• For car A:
  $x_A(t) = \alpha t + \beta t^2$ where $\alpha = 2.60 \, \text{m/s}$ and $\beta = 1.20 \, \text{m/s}^2$.
  Substituting the values: $x_A(t) = 2.60t + 1.20t^2$

• For car B:
  $x_B(t) = \gamma t^2 - \delta t^3$ where $\gamma = 2.80 \, \text{m/s}^2$ and $\delta = 0.20 \, \text{m/s}^3$.
  Substituting the values: $x_B(t) = 2.80t^2 - 0.20t^3$

Here are some possible questions we can explore:

1. At what time do the two cars meet? This involves solving the equation $x_A(t) = x_B(t)$.

2. What are the velocities of both cars as a function of time? This requires finding the first derivative of $x_A(t)$ and $x_B(t)$ with respect to time.

3. What are the accelerations of both cars as a function of time? This involves finding the second derivative of $x_A(t)$ and $x_B(t)$.

4. What is the distance between the two cars at a specific time $t$? This can be found using $|x_A(t) - x_B(t)|$.

5. What is the relative velocity of car A with respect to car B at a specific time $t$? This is found by taking the difference in their velocities.

Would you like to explore any of these questions or have more details on the problem?

Tip: When comparing two functions, setting them equal and solving for the variable can reveal critical points, such as when two moving objects meet.