If you walk for 1.66min at a speed of 1.22m/s and then run for 1.66min at 3.05m/s along a straight track, what is the average velocity?
analytical way:
total distance = 1.66*60*1.22 + 1.66*60*3.05 = 425.292m
total time = 1.66+1.66min = 199.2 sec
avg speed: 425.292m/199.2s = 2.135 m/s
easy way: equal times, so speed is average of 1.22 and 3.05 = 2.135 m/s
To find the average velocity, you need to calculate the total displacement and divide it by the total time taken.
Let's break down the problem:
1. For the walking portion:
- Time taken = 1.66 minutes = 1.66 * 60 = 99.6 seconds
- Speed = 1.22 m/s
- Displacement = speed * time taken = 1.22 m/s * 99.6 s = 121.272 m
2. For the running portion:
- Time taken = 1.66 minutes = 1.66 * 60 = 99.6 seconds
- Speed = 3.05 m/s
- Displacement = speed * time taken = 3.05 m/s * 99.6 s = 303.18 m
Now, let's find the total displacement and total time:
- Total displacement = displacement from walking + displacement from running
= 121.272 m + 303.18 m = 424.452 m
- Total time taken = time taken for walking + time taken for running
= 99.6 s + 99.6 s = 199.2 s
Finally, to find the average velocity:
- Average velocity = total displacement / total time taken
= 424.452 m / 199.2 s ≈ 2.13 m/s
Therefore, the average velocity for the given scenario is approximately 2.13 m/s.