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?

Explanation:

Speed is scalar (distance/time), velocity is vector (displacement/time). In 100m sprint, displacement = distance (straight path). In 400m sprint, displacement = 0 (starts/ends at same point), so velocity = 0, but speed > 0.

Answer:

Because velocity depends on displacement (vector), while speed depends on distance (scalar). For the 100-meter sprint, displacement equals distance (straight path), so velocity magnitude equals speed. For the 400-meter sprint, displacement is zero (starts and ends at the same point), so velocity is zero, but speed is non-zero. Thus, velocity and speed are the same only in the 100-meter sprint.