Honors AP Calculus / Mr. Hansen
3/2/2001

Name: ______________________

WARNING: Please do not peek until after you have tried to take the test under time pressure (50 minute limit).

1.(a)

2.5 m

(b)

–2 m (i.e., he has traveled 2 m backward)

(c)

v_av = –1 m/sec; avg. speed = 1.25 m/sec

2.(a)

16 sec
[Be sure to prove this is a min. One way is to check t when lower crossing point is 0, 12, and 20 m to right of a ^ dropped from Yoon’s starting point, since there is only one critical value. Because this is a non-calculator test, you need not compute t(0) and t(20); you need only show that the values exceed 16 sec.]

(b)

8 m

3.

Since v = <r cos t, r sin t>, |v| = Ö(r² cos² t + r² sin² t) = |r|. Also, we have
x´(t) = –r sin t
x´´(t) = –r cos t
y´(t) = r cos t
y´´(t) = –r sin t
\ (x´y´´ – x´´y´)/(|v|³) = (r² sin² t – (–r² cos² t))/(|r|³) = r²(1)/(|r|³) = 1/|r|, a constant (Q.E.D.)