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
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
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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.
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