To determine the student’s average velocity during a trip, we need to know two key pieces of information: the total displacement and the total time taken.

Key Concepts:

1. Average Velocity is defined as the total displacement (change in position) divided by the total time taken. It’s a vector quantity, meaning it has both magnitude and direction. $\text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}}$
2. If we only have the total distance traveled and not the direction or displacement, we can’t accurately calculate the average velocity, just the average speed.

Analysis of Options:

Part 1: Overall Trip

1. 16 mph and 56 mph: These values represent speed (magnitude only) but do not specify direction.
2. 36 mph south and 56 mph north: These are velocities because they include both magnitude and direction.
3. Not enough information is given: This option could be valid if displacement or time is missing.
4. 16 mph south: Similar to options 3 and 4 but with different magnitude.
5. 36 mph: Again, this is speed without direction.

Given these options, if no displacement or time data is provided, the answer could be 6. Not enough information is given.

Part 2: From Austin to Waco

1. 56 mph and 16 mph: These are speeds.
2. 36 mph south: This could be valid if it matches the direction of the trip.
3. Not enough information is given: This is possible if details are missing.
4. 56 mph north: This is a velocity.
5. 16 mph south: Same as option 3 but different magnitude.

For both parts, the answers depend on the specific direction and total displacement data given in the original problem.

Conclusion

If there's insufficient information about displacement or time, the answer for both parts is likely “Not enough information is given”.

Would you like further details or have any questions?

Relative Questions:

1. What is the difference between average speed and average velocity?
2. How can displacement be zero if distance traveled is not?
3. How does direction influence the calculation of average velocity?
4. Can average speed be equal to average velocity? If so, under what conditions?
5. How do you calculate the average speed for a round trip?

Tip: Always ensure you have both displacement and time data when calculating average velocity, as it’s a vector quantity requiring both magnitude and direction.