The distance traveled by the girl to complete half way around the circular track is equal to half of the circumference of the circle, which is:
d = (1/2) * 2πr = πr = π(10.0 m) = 31.4 m
The time taken by the girl to travel this distance is given as 15.0 s. Therefore, her average speed is:
average speed = distance / time = 31.4 m / 15.0 s ≈ 2.09 m/s
To calculate the magnitude of the girl's average velocity, we need to determine her displacement and divide it by the time taken. The girl's displacement is the straight-line distance from her starting point to her ending point, which is a distance of 2r = 20.0 m because she has traveled exactly half way around the circular track. Therefore, the magnitude of her average velocity is:
magnitude of average velocity = displacement / time = 20.0 m / 15.0 s ≈ 1.33 m/s
Note that the magnitude of the girl's average velocity is less than her average speed because her average velocity takes into account the direction of her motion, while her average speed does not.