a. Use the mean value theorem. 16 falls between 12 and 20, so

(Don't forget your units - 5 m/min^2)
b.  gives the Johanna's velocity at time
 gives the Johanna's velocity at time  . The magnitude of her velocity, or speed, is
. The magnitude of her velocity, or speed, is  . Integrating this would tell us the total distance she has traveled whilst jogging.
. Integrating this would tell us the total distance she has traveled whilst jogging.
The Riemann sum approximates the integral as

If you're not sure how this is derived: we're given 5 sample points, so we can cut the interval [0, 40] into 4 subintervals. The lengths of each subinterval are 12, 8, 4, and 16 (the distances between each sample point), and the height of the rectangle approximating the area under the plot of  is determined by the value of
 is determined by the value of  at each sample point, 200, 240, |-220| = 220, and 150.
 at each sample point, 200, 240, |-220| = 220, and 150.
c. Bob's velocity is given by  , so his acceleration is given by
, so his acceleration is given by  . We have
. We have

and at  his acceleration is
 his acceleration is  m/min^2.
 m/min^2.
d. Bob's average velocity over [0, 10] is given by the difference quotient,
 m/min
 m/min