When *v*(*t*) is positive, Brooke is moving East. When *v*(*t*) is negative, Brooke is moving West. When *v*(*t*) = 0, Brooke isn't moving at all. (a) Whenever *v*(*t*) = 0, Brooke is not moving. This occurs when *t* = 0, 3, 6, and 10. (b) Brooke is moving East whenever *v*(*t*) > 0. This corresponds to the intervals 0 < *t* < 3 and 6 < *t* < 10. We use the < sign instead of the ≤ sign because when *t* equals 0, 3, 6, or 10, Brooke isn't moving at all. Thus we we don't want to include those values of *t* in the intervals. (c) Brooke is moving West whenever *v*(*t*) < 0. This corresponds to the interval 3 < *t* < 6. (d) Brooke is moving most rapidly East when *v*(*t*) > 0 and |*v*(*t*)| is as large as possible (since speed is the absolute value of velocity). The largest positive value of velocity is *v*(2) = 3, so Brooke is moving most rapidly East when *t* = 2. (e) Brooke is moving most rapidly West when *v*(*t*) < 0 and |*v*(*t*)| is as large as possible. This means we're looking for the most negative value of velocity, which occurs when *t* = 4. (f) Brooke is moving most rapidly at *t* = 4, since |*v*(4)| = 4 mph is the largest absolute value the velocity attains on the time interval [0,10]. (g) Since speed is the absolute value of velocity, Brooke is speeding up whenever her velocity is getting farther away from zero. This occurs on the intervals (0,2), (3,4), and (6,9). (h) Brooke is slowing down whenever her velocity is getting closer to zero, since this means her speed |*v*(*t*)| is also getting closer to zero. This occurs on the intervals (2,3), (4,6), and (9,10). |