Exercises
UF Calculus Set 19
1. A particle is moving along a number line so that its position
s
(in meters) after
t
minutes is
given by the function
s
(
t
) = 16
t
3
+ 12
t
2

144
t t
≥
0
. Answer the following as directed.
(a) What is the position of the particle initially? after
1
minute? after
2
minutes?
(b) Write formulas for the velocity and acceleration of the particle at every time
t
.
(c) What is the average velocity of the particle during the ﬁrst two minutes?
(d) What is the instantaneous velocity of the particle initially? after two minutes?
(e) At what time(s) is the particle momentarily at rest? What is the acceleration of the parti
cle at that time?
(f) On what open interval(s) is the particle traveling in the negative direction?
(g) Find the displacement (change in position) of the particle on the interval
[0
,
2]
. What is
the overall distance traveled by the object on the interval?
(h) What is the furthest distance that the object has traveled away from its initial position
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 Spring '08
 ALL
 Calculus, Geometry, Revenue, Include units

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