Final answer:
To calculate Steve Prefontaine's acceleration, we'd use his initial speed at the 7.57 km mark and the formula for acceleration. However, without the final velocity or the distance covered during the acceleration, we cannot provide a numerical answer.
Step-by-step explanation:
To calculate Steve Prefontaine's acceleration over the 60-second interval, we need to use the kinematic equations for uniformly accelerated motion. If we assume that his instantaneous speed at the 7.57 km mark was the same as his overall average speed up to that point, we'd use this initial velocity (v_i) to find his final velocity (v_f) after the 60-second acceleration period, and then calculate the acceleration (a).
First, we find his initial velocity. Prefontaine completed 7.57 km in 25.0 minutes, so his average speed was v_i = d/t, where d is distance and t is time:
v_i = 7570 m / (25 min × 60 s/min) = 7570 m / 1500 s = 5.046 m/s
We are not given his final velocity, but we can calculate his acceleration if we assume he increases his speed uniformly over the next 60 seconds and then maintains this new, higher speed for the remainder of the race. The kinematic equation for acceleration is:
a = (v_f - v_i) / t
Without v_f, we can't find the exact value of a. However, we can express his final speed v_f in terms of his acceleration and the time he accelerated (60 s):
v_f = v_i + a(60 s)
Normally, as part of a complete solution, we would use additional information to solve for v_f or a. In this situation, we do not have enough information provided to produce a numerical answer for Steve Prefontaine's acceleration. We would need his final velocity or the distance covered during the 60 s acceleration period.