Compute your average velocity in the following two cases, (a) You walk 73.2 m at a speed of 1.22 m/s and then run 73.2 m at a speed of 2.85m/s along a straight track. (b) you walk for 1.00 min at a speed of 1.22 m/s and then run for 1.00 min at 3.05 m/s along a straight track. (c) Graph `x` versus t for both cases and indicate how the average velocity is found on the graph.

Answer

To compute the average velocity in the two cases described, we will follow these steps:

### Case (a)
1. **Calculate the time taken for walking**:
- Distance walked = 73.2 m
- Speed while walking (V1) = 1.22 m/s
- Time taken to walk (T1) = Distance / Speed = 73.2 m / 1.22 m/s
- T1 = 60 seconds (approx).

2. **Calculate the time taken for running**:
- Distance run = 73.2 m
- Speed while running (V2) = 2.85 m/s
- Time taken to run (T2) = Distance / Speed = 73.2 m / 2.85 m/s
- T2 = 25.68 seconds (approx).

3. **Calculate total displacement**:
- Total displacement = Distance walked + Distance run = 73.2 m + 73.2 m = 146.4 m.

4. **Calculate total time taken**:
- Total time = T1 + T2 = 60 s + 25.68 s = 85.68 s.

5. **Calculate average velocity**:
- Average velocity (V_avg) = Total displacement / Total time = 146.4 m / 85.68 s = 1.70 m/s (approx).

### Case (b)
1. **Calculate distance walked in 1 minute**:
- Speed while walking (V1) = 1.22 m/s
- Time walked = 1 minute = 60 seconds
- Distance walked (X1) = Speed * Time = 1.22 m/s * 60 s = 73.2 m.

2. **Calculate distance run in 1 minute**:
- Speed while running (V2) = 3.05 m/s
- Time run = 1 minute = 60 seconds
- Distance run (X2) = Speed * Time = 3.05 m/s * 60 s = 183 m.

3. **Calculate total displacement**:
- Total displacement = Distance walked + Distance run = 73.2 m + 183 m = 256.2 m.

4. **Calculate total time taken**:
- Total time = 1 minute + 1 minute = 2 minutes = 120 seconds.

5. **Calculate average velocity**:
- Average velocity (V_avg) = Total displacement / Total time = 256.2 m / 120 s = 2.135 m/s (approx).

### Case (c)
To graph `x` versus `t` for both cases:
1. **For Case (a)**:
- Plot points for walking and running.
- From (0,0) to (60, 73.2) for walking.
- From (60, 73.2) to (85.68, 146.4) for running.
- The slope of the line segments gives the velocities.

2. **For Case (b)**:
- Plot points for walking and running.
- From (0,0) to (60, 73.2) for walking.
- From (60, 73.2) to (120, 256.2) for running.
- Again, the slope of the line segments gives the velocities.

3. **Average Velocity on the Graph**:
- For both cases, the average velocity can be represented by the slope of the line connecting the starting point (0,0) to the endpoint (total time, total displacement).