A runner moves back and forth along a straight, one-dimensional track during an 8s interval. Her position x (measured from a fixed origin) is recorded at 2s intervals, producing the data in the table below.
Time t (s)
Position x (m)
0
0
2
10
4
15
6
9
8
−1
a) Calculate the total distance the runner travels between t=0s and t=8s.
b) Determine the runner’s displacement for the same time interval.
c) Compute the runner’s average speed over the 8s interval.
d) Compute the runner’s average velocity over the 8s interval.
e) For each of the four quantities you calculated in parts (a) through (d)—total distance, displacement, average speed, and average velocity—state whether it is a scalar or vector quantity and justify each classification with reference to magnitude and direction.