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AP@ CALCULUS AB

2003 SCORING GUIDELINES

Question 2

A particle moves along the ~axis so that its velocity at time t is given by

v( t) - ( t + 1) sin | ~].

At time t - O, the particle is at position ~ - 1.

(a) Find the acceleration of the particle at time t - 2. Is the speed of the particle increasing at t - 2?

Why or why not?

(b) Find all times t in the open interval O t 3 when the particle changes direction. Justify your

answer.

(c) Find the total distance traveled by the particle from time t - O until time t - 3.

(d) During the time interval O ~ t ~ 3, what is the greatest distance between the particle and the

origin? Show the work that leads to your answer.

(a) a(2) - vI(2) - 1.587 or 1.588 | 1 a(2)

v(2) - ,38in(2) O 2 ] 1 speed decreasing

Speed is decreasing since a(2) O and v(2) O . | with reason

(c) Distance - fo3l~ t)|dt - 4.333 or 4.334

:::l:: (distance particle travels

while velocity is negative)

(d)

Since the total distance from t - O to t - 3 is

4.334, the particle is stll-I to the left of the origin

at t - 3. Hence the greatest distance from the

origin is 2.265.

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