91Ó°ÊÓ

Average speed is a measure of how fast an object moves over a total distance, regardless of its direction. It is calculated by dividing the total distance traveled by the total time taken. Let's break it down with key points:

• Total Distance: This includes every bit of the journey's length no matter the direction, so here it would be east, west, or loops.
• Total Time: Converted into a consistent unit, typically hours, for accurate calculation.

In our problem, you drove two segments adding up to 85 km, taking 1 hour in total. Thus, the average speed is computed as:
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{85 \text{ km}}{1 \text{ h}} = 85 \text{ km/h}.\)
This metric doesn't consider the journey's path's geometry, only the start-to-finish span.

Average velocity is a vector quantity, meaning it includes both magnitude and direction. It is found by dividing the total displacement by the total time taken. Displacement, in contrast to distance, is the shortest path between the starting and ending points. This means it's a linear, direct measure.

• Displacement takes into account direction; thus, requires resolving distance parts into components using trigonometry when angles are involved.
  
• Total Time is still the journey's duration, making comparison consistent.

From the problem, your displacement is approximately 80.84 km, directed 28.15° south of west. Calculating average velocity:
\(\text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{80.84 \text{ km}}{1 \text{ h}} \approx 80.84 \text{ km/h}.\)
The direction matters here, indicating a south of west journey at about 28.15°, contrasting with scalar-only average speed.

The Pythagorean theorem helps link right triangle sides, useful for vector components in physics. It states that the square of the hypotenuse (long side) equals the sum of the squares of the other two sides.

Here's a simplified understanding applicable to our exercise:

• You have a right triangle when considering two directional movements like west and south.
• To find the resultant distance or straight-line displacement: You'll calculate like so: \(c = \sqrt{a^2 + b^2}\) where "c" is the hypotenuse.

In our problem, you combine the west component (70.96 km) and the south (38.57 km) using this. Compute your total displacement:
\[\text{Displacement} = \sqrt{70.96^2 + 38.57^2} \approx 80.84 \text{ km}.\]
This tells us precisely how far and in what vector direction you are from the start point, enhancing the depth of our journey's result beyond simple distance.