A track star sprints 50.0 m in 8.00 s, stops, turns directly around, and walks slowly back
to the starting line in 40.0 s. What are the average speed and velocity for his round trip?
average speed=distancetotal/totaltime
average velocity=totaldisplacement/time=0
To find the average speed, we need to calculate the total distance covered and divide it by the total time taken.
Distance covered during the sprint = 50.0 m
Distance covered during the walk back = 50.0 m (since the track star retraces his steps)
Total distance covered = 50.0 m + 50.0 m = 100.0 m
Total time taken = Time taken for the sprint + Time taken for the walk back
= 8.00 s + 40.0 s = 48.0 s
Average speed = Total distance covered / Total time taken
= 100.0 m / 48.0 s
≈ 2.08 m/s
Now let's find the velocity, which takes into account the direction of motion.
Velocity is a vector quantity, meaning it has magnitude (speed) and direction.
Since the track star sprints 50.0 m in 8.00 s and then walks back along the same path, the displacement (change in position) is zero. The starting and ending positions are the same.
Therefore, the average velocity is zero, because the displacement is zero and the time taken is 48.0 s.
To find the average speed and velocity for the track star's round trip, we need to understand the basic definitions of speed and velocity.
Average Speed: It is the total distance covered divided by the total time taken.
Average Velocity: It is the displacement (change in position) divided by the total time taken.
Given data:
- Distance covered while sprinting forward (one way): 50.0 m
- Time taken while sprinting forward: 8.00 s
- Time taken while walking back: 40.0 s
Now, let's find the average speed and velocity step by step:
1. Calculate the total distance covered:
Since the track star sprints forward 50.0 m and then walks back the same distance, the total distance covered is: 50.0 m + 50.0 m = 100.0 m.
2. Calculate the total time taken:
The total time taken is the sum of the time taken while sprinting forward and the time taken while walking back: 8.00 s + 40.0 s = 48.0 s.
3. Calculate the average speed:
Average Speed = Total Distance / Total Time
Average Speed = 100.0 m / 48.0 s ≈ 2.08 m/s
Therefore, the average speed for the round trip is approximately 2.08 m/s.
4. Calculate the average velocity:
To determine the average velocity, we need to find the displacement, which is the net change in position from the starting point to the ending point.
Since the track star returns to the starting line, the displacement is 0 (starting and ending at the same point).
Average Velocity = Displacement / Total Time
Average Velocity = 0 m / 48.0 s = 0 m/s
Therefore, the average velocity for the round trip is 0 m/s.
In summary, the track star's average speed for the round trip is approximately 2.08 m/s, while the average velocity is 0 m/s.