\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
\[ \text{Average Velocity} = \frac{\text{Displacement}}{\text{Total Time}} \]
1. Average Speed from A to B:
The total distance from A to B is 300 m, and the total time is 150 seconds.
\[ \text{Average Speed from A to B} = \frac{300 \, \text{m}}{150 \, \text{s}} = 2 \, \text{m/s} \]
2. Average Velocity from A to B:
Since Joseph is moving in a straight line from A to B, the displacement is equal to the distance of 300 m. The time is 150 seconds.
\[ \text{Average Velocity from A to B} = \frac{300 \, \text{m}}{150 \, \text{s}} = 2 \, \text{m/s} \]
1. Average Speed from A to C:
The total distance covered is the sum of the distance from A to B (300 m) and the distance from B to C (100 m). The total time is the sum of the time from A to B (150 seconds) and the time from B to C (60 seconds).
\[ \text{Total Distance from A to C} = 300 \, \text{m} + 100 \, \text{m} = 400 \, \text{m} \] \[ \text{Total Time from A to C} = 150 \, \text{s} + 60 \, \text{s} = 210 \, \text{s} \] \[ \text{Average Speed from A to C} = \frac{400 \, \text{m}}{210 \, \text{s}} \approx 1.90 \, \text{m/s} \]
2. Average Velocity from A to C:
The displacement from A to C is the straight-line distance from A to C, which is 200 m (since Joseph jogged 300 m in one direction and 100 m back).
\[ \text{Average Velocity from A to C} = \frac{200 \, \text{m}}{210 \, \text{s}} \approx 0.95 \, \text{m/s} \]