A100-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?

The speed and velocity of the body for 100-m track is same due to same distance and displacement. And due to unequal distance and displacement, the speed and velocity for 400 m track is not same.

Given data:

The value of length of first track is, s = 100 m.

The length of second track is, s' = 400 m.

The speed is defined as the total length of path covered during a journey in a given time (say t). And velocity is termed as the displacement covered by the body in a given time.

A 100-meter track of straight side resembles a linear motion in one-dimension. In this, the body is covering the 100 m distance and is not coming back. This means the distance and displacement for the body is same. Hence, the speed and velocity of the body for 100-m track is also same.

On the other hand, 400-meter round track resembles a circular motion of a body. In this case, the body has covered some distance but since it returns to its initial state, therefore the displacement becomes zero. Hence, the speed and velocity for the body undergoing one complete lap around a 400 m racetrack is not same.

Thus, we conclude that  the speed and velocity of the body for 100-m track is same due to same distance and displacement. But different is case of 400 m track, due to unequal distance and displacement.

Learn more about the distance and displacement here:

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