A runner jogs a along a straight road (in the `+x` direction) for `30 min`, travelling a distance of `6 km`. She then turns around and walks back towards her starting point for `20 min`, travelling `2 km` during this time. State true// false:
a. The final displacement of the entire trip is `0`. `16 km min^(-1)` .
b. Her average speed for the entire is `0.16 km min^(-1)`.
c. The average velocity for the entire trip is `0.4 km min^(-1)`.
d. The runner`s average velocity while jogging is `0.4 km min^(-1)`.
e. Her average velocity while walking is `0.1 km min^(-1)`.

Explanation

To solve the problem, let's analyze the runner's journey step by step.

### Step 1: Calculate the total distance traveled
The runner jogs 6 km in the positive x direction and then walks back 2 km towards the starting point.

- **Total distance** = Distance jogged + Distance walked back
- **Total distance** = 6 km + 2 km = 8 km

### Step 2: Calculate the total time taken
The time taken for jogging is 30 minutes and the time taken for walking back is 20 minutes.

- **Total time** = Time jogging + Time walking back
- **Total time** = 30 minutes + 20 minutes = 50 minutes

### Step 3: Calculate the final displacement
Displacement is the shortest distance from the initial position to the final position. The runner starts at point O (0 km), jogs to point P (6 km), and then walks back to point Q (4 km).

- **Final displacement** = Final position - Initial position
- **Final displacement** = 4 km - 0 km = 4 km

### Step 4: Determine if the statements are true or false
Now, let's evaluate each statement:

a. **The final displacement of the entire trip is 0.16 km.**
- **False**. The final displacement is 4 km.

b. **Her average speed for the entire trip is 0.16 km/min.**
- **True**. Average speed = Total distance / Total time = 8 km / 50 min = 0.16 km/min.

c. **The average velocity for the entire trip is 0.4 km/min.**
- **False**. Average velocity = Total displacement / Total time = 4 km / 50 min = 0.08 km/min.

d. **The runner's average velocity while jogging is 0.4 km/min.**
- **True**. Average velocity while jogging = Distance jogged / Time jogging = 6 km / 30 min = 0.2 km/min.

e. **Her average velocity while walking is 0.1 km/min.**
- **True**. Average velocity while walking = Distance walked / Time walking = 2 km / 20 min = 0.1 km/min.

### Summary of the statements:
- a: False
- b: True
- c: False
- d: False
- e: True