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?

Sure, let's break it down step by step:

1. Understanding Speed and Velocity:

   • Speed is a scalar quantity that refers to how fast an object is moving. It is the rate at which an object covers distance.
   • Velocity is a vector quantity that refers to the rate at which an object changes its position. It includes both speed and direction.

2. 100-Meter Sprint:

   • In a 100-meter sprint, the race is run in a straight line.
   • Since the direction does not change, the distance covered (100 meters) is the same as the displacement (100 meters in a straight line).
   • Therefore, the speed (distance/time) and the magnitude of the velocity (displacement/time) are the same because the direction is constant and straight.

3. 400-Meter Sprint:

   • In a 400-meter sprint, the race is run around a track, which is typically an oval shape.
   • The distance covered is 400 meters, but because the runner returns to the starting point, the displacement is zero (the initial and final positions are the same).
   • Speed is calculated as distance/time, so it will be based on the 400 meters.
   • Velocity, however, is calculated as displacement/time. Since the displacement is zero, the average velocity over the entire race is zero.

4. Conclusion:

   • For the 100-meter sprint, both speed and velocity are the same because the direction is constant and the displacement equals the distance.
   • For the 400-meter sprint, speed and velocity differ because the displacement is zero, making the average velocity zero, while the speed is based on the total distance covered.

This explains why velocity and speed are the same for a 100-meter sprint but not for a 400-meter sprint.