Final answer:
The runner's average acceleration from 0 to 4 seconds is 2.5 m/s², from 4 to 8 seconds is 0 m/s² as she maintains a constant velocity, and from 8 to 12.7 seconds is -0.426 m/s² as she decelerates.
Step-by-step explanation:
To determine the runner's average acceleration over the given time periods, we'll use the formula for acceleration (a) which is the change in velocity (Δv) divided by the change in time (Δt): a = Δv / Δt.
From 0 to 4 seconds:
Initial velocity (u) is 0 m/s (since the runner starts from rest), final velocity (v) is 10 m/s, and the time taken (t) is 4 seconds. Thus, the average acceleration (a) is (10 m/s - 0 m/s) / 4 s = 2.5 m/s².
From 4 to 8 seconds:
The velocity remains constant at 10 m/s, so there is no change in velocity. Hence, the acceleration is 0 m/s².
From 8 to 12.7 seconds:
The velocity decreases from 10 m/s to 8 m/s over 4.7 seconds. The average acceleration is (8 m/s - 10 m/s) / 4.7 s = -0.426 m/s², which is a negative value indicating deceleration.
The runner's average acceleration can be calculated by dividing the change in velocity by the change in time for each time period.
From 0 to 4s: The runner accelerated from 0 m/s to 10 m/s, so the change in velocity is 10 m/s. The change in time is 4s, so the average acceleration is 10 m/s divided by 4s, which is 2.5 m/s².
From 4 to 8s: The runner maintained a velocity of 10 m/s, so there was no change in velocity. The change in time is 4s, so the average acceleration is 0 m/s divided by 4s, which is 0 m/s².
From 8 to 12.7s: The runner decelerated from 10 m/s to 8 m/s, so the change in velocity is -2 m/s. The change in time is 4.7s, so the average acceleration is -2 m/s divided by 4.7s, which is approximately -0.43 m/s².