Particle Motion Revisited
Directions:
Complete on separate paper.
Each question should be done on a separate side of the
page (you will use two pieces of paper for this assignment). These will be “graded” AP style. Show all
integrals or explanations as if this was the AP Exam.
NO CALCULATOR
#s 2 and 3, CALCULATOR ACTIVE
2) A particle moves along the x-axis so that its velocity v at time t, for 0 < t < 5, is given by v(t) = ln (t2 – 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.
(e) Find the total distance traveled by the particle for 0 < t < 5.
3) Two runners, A and B, run on a straight racetrack for
0 < t < 10 seconds. The graph shows the velocity, in
meters per second, of Runner A. The velocity, in
meters per second, of Runner B is given by the
function
vt   24t .
2t  3
(a) Find the velocity of Runner A and the velocity
of Runner B at time t = 2 seconds. Indicate
units of measure.
(b) Find the acceleration of Runner A and the acceleration of Runner B at time t = 2 seconds. Indicate
units of measure.
(c) Find the total distance run by Runner A and the total distance run by Runner B over the time interval
0 < t < 10 seconds. Indicate units of measure.
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