a 100 - meter sprint is a race using only the straight side of a racetrack. a 400 - meter sprint is a race…

Answer:

Velocity and speed are the same for a 100 - m sprint because it is a straight - line motion. In straight - line motion, the distance traveled is equal to the magnitude of the displacement. Since speed is the rate of change of distance ($s=\frac{d}{t}$) and velocity is the rate of change of displacement ($v = \frac{\Delta x}{t}$), when $d=\vert\Delta x\vert$, speed and velocity have the same magnitude. For a 400 - m sprint, the runner makes one complete lap around a racetrack. When the runner finishes the lap, the displacement is zero (because the starting and ending points are the same), while the distance traveled is 400 meters. So, speed is non - zero ($s=\frac{400}{t}$) but velocity is zero ($v=\frac{0}{t} = 0$) as displacement is zero.

Explanation:

Step1: Define speed and velocity

Speed is rate of distance change ($s=\frac{d}{t}$), velocity is rate of displacement change ($v=\frac{\Delta x}{t}$).

Step2: Analyze 100 - m sprint

In 100 - m straight sprint, $d=\vert\Delta x\vert = 100$ m, so $s = v$.

Step3: Analyze 400 - m sprint

In 400 - m lap, $d = 400$ m, $\Delta x=0$ m, so $s=\frac{400}{t}\neq v = 0$.