Compute your average velocity in the following two cases: (a) You walk 73.6 m at a speed of 1.79 m/s and then run 73.6 m at a speed of 4.31 m/s along a straight track. (b) You walk for 1.00 min at a speed of 1.79 m/s and then run for 1.30 min at 4.31 m/s along a straight track.
To compute average velocity, we need to use the formula:
Average Velocity = Total Distance / Total Time
(a) In the first case, we are given the distances walked and run, as well as the speeds. We need to find the total distance and total time.
Total Distance = Distance walked + Distance run
Total Distance = 73.6 m + 73.6 m = 147.2 m
Total Time = Time taken to walk + Time taken to run
Total Time = Distance walked / Speed of walking + Distance run / Speed of running
Total Time = 73.6 m / 1.79 m/s + 73.6 m / 4.31 m/s
Now, we can calculate the average velocity by dividing the total distance by the total time obtained:
Average Velocity = Total Distance / Total Time
Average Velocity = 147.2 m / (73.6 m / 1.79 m/s + 73.6 m / 4.31 m/s)
(b) In the second case, we are given the times taken to walk and run, as well as the speeds. We need to convert the given times to distances and then find the total distance and total time.
Distance walked = Speed of walking * Time taken to walk
Distance walked = 1.79 m/s * 1.00 min = 1.79 m/s * 60 s = 107.4 m
Distance run = Speed of running * Time taken to run
Distance run = 4.31 m/s * 1.30 min = 4.31 m/s * 78 s = 336.18 m
Total Distance = Distance walked + Distance run
Total Distance = 107.4 m + 336.18 m = 443.58 m
Total Time = Time taken to walk + Time taken to run
Total Time = Time taken to walk in seconds + Time taken to run in seconds
Total Time = 1.00 min * 60 s + 1.30 min * 60 s
Now, we can calculate the average velocity by dividing the total distance by the total time obtained:
Average Velocity = Total Distance / Total Time
Average Velocity = 443.58 m / (1.00 min * 60 s + 1.30 min * 60 s)
To compute average velocity, we need to divide the total displacement by the total time taken.
(a) In the first case, you walk 73.6 m and then run 73.6 m, so the total displacement is 2 * 73.6 m = 147.2 m.
The time taken to walk is given as the ratio of distance to speed, which is 73.6 m / 1.79 m/s = 41.1 s.
Similarly, the time taken to run is 73.6 m / 4.31 m/s = 17.1 s.
The total time taken is 41.1 s + 17.1 s = 58.2 s.
Therefore, the average velocity is the total displacement divided by the total time taken: 147.2 m / 58.2 s = 2.53 m/s.
(b) In the second case, you walk for 1.00 min and then run for 1.30 min.
Using the same reasoning as above, the total displacement is 2 * 73.6 m = 147.2 m.
The time taken to walk is 1.00 min = 60 s.
The time taken to run is 1.30 min = 78 s.
The total time taken is 60 s + 78 s = 138 s.
Therefore, the average velocity is the total displacement divided by the total time taken: 147.2 m / 138 s = 1.07 m/s.