To solve this problem, we'll break it down into two parts based on the given information:

Given:

• Acceleration $a = 3.30 \, \text{m/s}^2$
• Initial velocity $v_0 = -6.80 \, \text{m/s}$
• Final velocity $v_f = 13.6 \, \text{m/s}$
• We need to find the displacement and the total distance traveled.

Part 1: Displacement

We can use the following kinematic equation to find the displacement $d$:

$v_f^2 = v_0^2 + 2ad$

Rearrange the equation to solve for displacement $d$:

$d = \frac{v_f^2 - v_0^2}{2a}$

Substituting the known values:

$d = \frac{(13.6)^2 - (-6.80)^2}{2 \times 3.30}$

Now, let's calculate:

$d = \frac{184.96 - 46.24}{6.60}$

$d = \frac{138.72}{6.60}$

$d \approx 21.0 \, \text{m}$

Part 2: Total Distance

Since the block starts with a negative velocity and then accelerates positively, the total distance will be calculated by taking the absolute value of the displacement, considering any changes in direction. However, in this case, the block only moves in one direction (no reverse motion), so the displacement itself represents the total distance traveled.

Thus, the total distance traveled is the same as the displacement: $21.0 \, \text{m}$.

Final Answers:

1. Displacement during the time interval: $d = 21.0 \, \text{m}$
2. Total distance traveled: $21.0 \, \text{m}$

Let me know if you'd like further explanations or additional details!

Here are some related questions to explore:

1. How would the displacement change if the block had been moving on a surface with friction?
2. What would happen if the acceleration was negative (deceleration)?
3. How do you calculate displacement if velocity is given as a function of time?
4. What would be the time it took for the block to reach the final velocity?
5. How can we determine the work done on the block during this interval?

Tip: When working with kinematic equations, ensure that all units are consistent, typically in meters, seconds, and meters per second for velocity.