posted by anonymous .
A runner circles a track of radius 50 m in 50 s moving at a constant rate. If the runner was initially moving north, what has been the runner's average acceleration when halfway around the track?
First get the speed, which is constant.
It is 2 pi*50/50 = 6.28 m/s
The DIRECTION of velocity changes 180 degrees in the time it take to go half way around the track, 25 s. The velcoity changes by 12.56 m/s, from 6.28 to -6.28.
The AVERAGE acceleration is the change in the velocity vector divided by the time, which is
a(av) = 2*6.28/25 = 0.502 m/s^2
The value of the acceleration scalar is always V^2/R = 0.789 m/s^2, but its direction is constantly changing. I don't believe that is what they area after.