38. A particle moves along the x axis. Its position is giv 4t2, with x in meters and w by the equation x = 2 + 3t tin seconds. Determine (a) its position when it changes direction and (b) its velocity when it returns to the position it had at t = 0. 20 à glider of length moves through a stationary pho- 1

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Chapter1: Units, Trigonometry. And Vectors
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54
Chapter 2 Motion in One Dimension
displacement. (a) Draw a coordinate system for this
situation. (b) What analysis model is most appropri-
ate for describing this situation? (c) From the analysis
model, what equation is most appropriate for finding
the acceleration of the speedboat? (d) Solve the equa-
tion selected in part (c) symbolically for the boat's
acceleration in terms of u, v, and Ax. (e) Substitute
numerical values to obtain the acceleration numeri-
cally. (f) Find the time interval mentioned above.
38. A particle moves along the x axis. Its position is given
w by the equation x= 2 + 3t - 4t², with x in meters and
tin seconds. Determine (a) its position when it changes
direction and (b) its velocity when it returns to the
position it had at t = 0.
l
39. A glider of length moves through a stationary pho-
togate on an air track. A photogate (Fig. P2.39) is
a device that measures the time interval Ata dur-
ing which the glider blocks a beam of infrared light
passing across the photogate. The ratio v₁ = e/At& is
the average velocity of the glider over this part of its
motion. Suppose the glider moves with constant accel-
eration. (a) Argue for or against the idea that Va
is
equal to the instantaneous velocity of the glider when
it is halfway through the photogate in space. (b) Argue
for or against the idea that va is equal to the instanta-
neous velocity of the glider when it is halfway through
the photogate in time.
the
els c
*
42. At a
with
and
mo
tra
wh
(b)
tin
ar
en
as
43. Fi
of
of
Р
la
e
u
li
t
t
44.
M
Transcribed Image Text:54 Chapter 2 Motion in One Dimension displacement. (a) Draw a coordinate system for this situation. (b) What analysis model is most appropri- ate for describing this situation? (c) From the analysis model, what equation is most appropriate for finding the acceleration of the speedboat? (d) Solve the equa- tion selected in part (c) symbolically for the boat's acceleration in terms of u, v, and Ax. (e) Substitute numerical values to obtain the acceleration numeri- cally. (f) Find the time interval mentioned above. 38. A particle moves along the x axis. Its position is given w by the equation x= 2 + 3t - 4t², with x in meters and tin seconds. Determine (a) its position when it changes direction and (b) its velocity when it returns to the position it had at t = 0. l 39. A glider of length moves through a stationary pho- togate on an air track. A photogate (Fig. P2.39) is a device that measures the time interval Ata dur- ing which the glider blocks a beam of infrared light passing across the photogate. The ratio v₁ = e/At& is the average velocity of the glider over this part of its motion. Suppose the glider moves with constant accel- eration. (a) Argue for or against the idea that Va is equal to the instantaneous velocity of the glider when it is halfway through the photogate in space. (b) Argue for or against the idea that va is equal to the instanta- neous velocity of the glider when it is halfway through the photogate in time. the els c * 42. At a with and mo tra wh (b) tin ar en as 43. Fi of of Р la e u li t t 44. M
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