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?
Velocity and speed are the same for a 100-meter sprint because the race takes place in a straight line, meaning the distance traveled is the same as the displacement. Therefore, since velocity is defined as the rate of change of displacement, velocity and speed are the same in this case.
On the other hand, in a 400-meter sprint, the runner makes one complete lap around the track, meaning the distance traveled is greater than the displacement. Since speed is defined as the rate of change of distance traveled, the speed will be higher than the average velocity for this race. This is because velocity takes into account the direction of motion (in this case, along the curved path of the track), whereas speed only considers the total distance covered.