Estimate the magnitude of the acceleration 𝑎track for the same athlete falling while running at full speed and coming to rest on a running track made from a synthetic material.

Question

The severity of many sports injuries is related to the magnitude of the acceleration that an athlete's body undergoes as it comes to rest, especially when joints (such as ankles and knees) are not properly aligned during falls.

1. Estimate the magnitude of the acceleration mud of a world‑class athlete who falls while running at full speed and comes to rest on a muddy field. Assume the runner falls face first and does not roll.
2. Estimate the magnitude of the acceleration track for the same athlete falling while running at full speed and coming to rest on a running track made from a synthetic material.

(I already got the #1 but I don't know what I'm doing wrong for #2)

Answer 1

1) first case

a= (v-u)/t

Where:

1. a is the acceleration.
2. v is the final velocity, which is 0 m/s (as the athlete comes to rest).
3. u is the initial velocity, which depends on the athlete's speed while running.
4. t is the time it takes to come to rest.

This formula describes the deceleration (negative acceleration) that the athlete experiences during the fall on the muddy field. so the answer for question 1 is a=(0-u)/t a=-u/t

2) second case

a= (v-u)/t

Where:

1. a is the acceleration.
2. v is the final velocity, which depends on the athlete's speed while running.
3. u is the initial velocity, which is 0 m/s (as the athlete starts from rest).
4. t is the time it takes to come to rest.

This formula describes the acceleration (positive) that the athlete experiences after starting back up running. so the answer for question 2 is a= (v-0)/t a=v/t