In the image, a problem is presented involving a cross-country skier moving between four locations (A, B, C, and D) in a 3-minute time period. Here's how to solve the problem:

Given Information:

• The skier moves from location A to B to C to D.
• The total time of the trip is 3 minutes.
• The distances between the locations are marked on a horizontal scale in meters:
  • A is at 0 meters (t=0 min).
  • B is at 160 meters (t=1 min).
  • C is at 40 meters (t=2 min).
  • D is at 120 meters (t=3 min).

To find:

• Average Speed (in meters per minute)
• Average Velocity (in meters per minute)

1. Average Speed:

• Average speed is defined as the total distance traveled divided by the total time taken.
• The skier's path:
  • From A to B: 160 meters
  • From B to C: 160 - 40 = 120 meters
  • From C to D: 120 - 40 = 80 meters
  • Total distance = 160 + 120 + 80 = 360 meters
• Total time = 3 minutes

So, the average speed = $\frac{360 \text{ meters}}{3 \text{ minutes}} = 120 \text{ meters per minute}$.

2. Average Velocity:

• Average velocity is defined as the total displacement (straight line from start to finish) divided by the total time.
• The skier starts at A (0 meters) and finishes at D (120 meters).
• Total displacement = 120 meters - 0 meters = 120 meters
• Total time = 3 minutes

So, the average velocity = $\frac{120 \text{ meters}}{3 \text{ minutes}} = 40 \text{ meters per minute}$.

Final Answers:

• Average Speed = 120 meters per minute
• Average Velocity = 40 meters per minute

Let me know if you'd like any further details or have questions.

Here are some related questions:

1. What is the difference between average speed and average velocity in general terms?
2. How would the average speed change if the skier had taken a different path but still ended at location D in 3 minutes?
3. How is displacement different from total distance in physics?
4. If the skier took a longer route to reach the same final position, what would happen to the average velocity?
5. Can the average velocity ever be greater than the average speed?

Tip: Remember, velocity is a vector quantity (it has direction), while speed is a scalar (it only has magnitude).