Unformatted text preview: 3 AP® CALCULUS AB
2005 SCORING GUIDELINES (Form B)
Question 3 A particle moves along the xaxis so that its velocity v at time t, for 0 ≤ t ≤ 5, is given by ( ) v( t ) = ln t 2 − 3t + 3 . The particle is at position x = 8 at time t = 0.
(a) Find the acceleration of the particle at time t = 4.
(b) Find all times t in the open interval 0 < t < 5 at which the particle changes direction. During which
time intervals, for 0 ≤ t ≤ 5, does the particle travel to the left?
(c) Find the position of the particle at time t = 2.
(d) Find the average speed of the particle over the interval 0 ≤ t ≤ 2. (a) 5
a( 4 ) = v′( 4 ) =
7 (b) v( t ) = 0 1 : answer ⎧ 1 : sets v( t ) = 0
⎪
3 : ⎨ 1 : direction change at t = 1, 2
⎪ 1 : interval with reason
⎩ 2 t − 3t + 3 = 1
t 2 − 3t + 2 = 0
( t − 2 ) ( t −1) = 0
t = 1, 2
v( t ) > 0 for 0 < t < 1
v( t ) < 0 for 1 < t < 2
v( t ) > 0 for 2 < t < 5
The particle changes direction when t = 1 and t = 2.
The particle travels to the left when 1 < t < 2. (c) ( ∫0 ln ( u − 3u + 3) du
2
s ( 2 ) = 8 + ∫ ln ( u 2 − 3u + 3) du
0
s( t ) = s( 0 ) + t = 8.368 or 8.369 (d) ) ⎧ 1 : 2 ln u 2 − 3u + 3 du
∫0
⎪
⎪
3: ⎨
1 : handles initial condition
⎪
⎪
⎩ 1 : answer 2 12
v( t ) dt = 0.370 or 0.371
2 ∫0 ⎧ 1 : integral
2: ⎨
⎩ 1 : answer Copyright © 2005 by College Board. All rights reserved.
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2005 SCORING GUIDELINES (Form B)
Question 4 The graph of the function f above consists of three line
segments.
(a) Let g be the function given by g ( x ) = x ∫− 4 f ( t ) dt. For each of...
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This note was uploaded on 10/01/2009 for the course OC 9876 taught by Professor Dq during the Spring '09 term at UC Merced.
 Spring '09
 Dq

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