Question
A 100-meter sprint is a race using only the straight side of a racetrack. A 400-meter sprint is a race that makes one complete lap around a racetrack. Why are velocity and speed the same for a 100-m sprint but not a 400-m sprint?
Answers
GPT-4o mini
To understand why velocity and speed are the same for a 100-meter sprint but not for a 400-meter sprint, we need to differentiate between speed and velocity:
1. **Speed** is a scalar quantity that refers to how fast an object is moving, regardless of direction. It is calculated as the total distance traveled divided by the total time taken.
2. **Velocity**, on the other hand, is a vector quantity that includes both speed and direction. It is calculated as the displacement (change in position) divided by the total time taken.
### 100-Meter Sprint:
- During a 100-meter sprint, the runner starts at one point and finishes at another point that is 100 meters away in a straight line. The displacement in this case is also 100 meters (from the starting line to the finish line).
- Since the direction is consistent and linear, the average speed and average velocity can be calculated easily. For instance, if the runner completes the sprint in 10 seconds, both speed and velocity would be 10 m/s with the direction pointing toward the finish line.
### 400-Meter Sprint:
- In a 400-meter sprint, which is one lap around a standard track, the runner returns to the starting point after completing the lap.
- The total distance covered is 400 meters, but the displacement is zero because the start and endpoint are the same. Displacement is a measure of the shortest distance from the initial position to the final position, and in this case, that distance is zero.
- As a result, if the runner takes the same 10 seconds to complete the 400 meters, the average speed would still be 40 m/s (400 meters / 10 seconds), but the average velocity would be 0 m/s due to zero displacement (0 meters / 10 seconds).
### Conclusion:
In summary, for the 100-meter sprint, both speed and velocity are the same because displacement is equal to the distance traveled. In contrast, for the 400-meter sprint, speed and velocity differ because while distance is non-zero, the displacement is zero due to returning to the original starting point.
1. **Speed** is a scalar quantity that refers to how fast an object is moving, regardless of direction. It is calculated as the total distance traveled divided by the total time taken.
2. **Velocity**, on the other hand, is a vector quantity that includes both speed and direction. It is calculated as the displacement (change in position) divided by the total time taken.
### 100-Meter Sprint:
- During a 100-meter sprint, the runner starts at one point and finishes at another point that is 100 meters away in a straight line. The displacement in this case is also 100 meters (from the starting line to the finish line).
- Since the direction is consistent and linear, the average speed and average velocity can be calculated easily. For instance, if the runner completes the sprint in 10 seconds, both speed and velocity would be 10 m/s with the direction pointing toward the finish line.
### 400-Meter Sprint:
- In a 400-meter sprint, which is one lap around a standard track, the runner returns to the starting point after completing the lap.
- The total distance covered is 400 meters, but the displacement is zero because the start and endpoint are the same. Displacement is a measure of the shortest distance from the initial position to the final position, and in this case, that distance is zero.
- As a result, if the runner takes the same 10 seconds to complete the 400 meters, the average speed would still be 40 m/s (400 meters / 10 seconds), but the average velocity would be 0 m/s due to zero displacement (0 meters / 10 seconds).
### Conclusion:
In summary, for the 100-meter sprint, both speed and velocity are the same because displacement is equal to the distance traveled. In contrast, for the 400-meter sprint, speed and velocity differ because while distance is non-zero, the displacement is zero due to returning to the original starting point.