1. Part (a)
m =
8 - 7
m =
-0.1
Acceleration is the derivative of velocity. We have a velocity graph, and the derivative is the slope.
This question is simply asking for the slope at t = 7.5 min.
Caryn’s acceleration at 7.5 seconds is -0.1 miles/minute2.

2. v(t) dt is the total distance (in miles) that
Part (b) 12
v(t) dt =
1.4 .2
1.8 miles .2
v(t) dt is the total distance (in miles) that
Caryn traveled during the entire 12 minutes. 12

3. Part (c)
Caryn turns around to go back home 2 minutes after initially leaving for school.
You can tell she changed direction at t = 2 because her velocity went from positive to negative there.

4. Part (d) 1.4 Remember—she had to return home to get her book.
From Part (b), we know that Caryn lives 1.4 miles from school.

5. Part (d)
From Part (b), we know that Caryn lives 1.4 miles from school.
w(t) dt = 1.6 12
Larry lives 1.6 miles from school, so Caryn is closer.