In April 1974, Steve Prefontaine completed a 10 km race in a time of 27 min , 43.6 s . Suppose "Pre" was at the 7.15 km mark at a time of 25.0 min . If he accelerated for 60 s and then maintained his increased speed for the remainder of the race, calculate his acceleration over the 60 s interval. Assume his instantaneous speed at the 7.15 km mark was the same as his overall average speed up to that time.

I was unsure how to do this but I attempted it about 4 times. The answers I calculated are 0.00397, 5.1, 4.9, and 0.006.

Use this as a sample problem:

https://answers.yahoo.com/question/index?qid=20140117202925AA400ns

To calculate Steve Prefontaine's acceleration over the 60-second interval, we need to use the formula for average acceleration:

average acceleration = (final velocity - initial velocity) / time interval

First, let's determine the initial velocity at the 7.15 km mark. We know that his instantaneous speed at the 7.15 km mark was the same as his overall average speed up to that time. So, we can calculate his average speed over the first 7.15 km using the given time interval of 25.0 min:

average speed = distance / time
average speed = 7.15 km / (25 min + 43.6 sec / 60)
average speed = 24.83 km/h

Since speed is the distance traveled divided by the time taken, we can convert the average speed to m/s:

average speed = (24.83 km/h) * (1000 m/km) / (3600 s/h)
average speed = 6.897 m/s

Now, let's determine the final velocity after the acceleration phase. We know that Steve Prefontaine maintained his increased speed for the remaining distance (10 km - 7.15 km = 2.85 km). We can calculate his increased speed using the total time taken (27 min 43.6 sec - 25 min = 2 min 43.6 sec) and adding it to the average speed:

increased speed = average speed + (distance / time)
increased speed = 6.897 m/s + (2.85 km / ((2 min + 43.6 sec) / 60))
increased speed = 6.897 m/s + (2.85 km / (2.727 min))
increased speed = 6.897 m/s + (1044.35 m / 2.727 min)
increased speed = 6.897 m/s + 383.11 m/min
increased speed = 6.897 m/s + (383.11 m/min * (1 min / 60 sec))
increased speed = 6.897 m/s + 6.385 m/s
increased speed = 13.282 m/s

Finally, we can calculate the acceleration using the average acceleration formula:

average acceleration = (final velocity - initial velocity) / time interval
average acceleration = (13.282 m/s - 6.897 m/s) / 60 s
average acceleration = 6.385 m/s / 60 s
average acceleration = 0.106 m/s^2

So, the correct answer for Steve Prefontaine's acceleration over the 60-second interval is approximately 0.106 m/s^2.