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.
![The Notion of Deriving
Deriving an equation (or a statement) is more than just asserting it. It's
showing how it must be true (and anything contrary must be false).
One doesn't understand the material as long as one is limited to
memorizing statements or equations, without being able to connect
them.
As a further, practical thing, understanding the connection makes it less
likely that one would use an equation when it doesn't apply. In
particular, one would avoid the "equations of constant acceleration"
anytime one had non-constant acceleration.
In this assignment, I assign you to derive the "equations of constant
acceleration" -- all but one that I will derive. We will use 0, w, and a,
satisfying these definitions:
dw
de
and
a =
dt
W =
dt
and one special case: a is constant. (You should spot the false step
when a is non-constant.) w and 0 are functions of time: w(t) and 0(t).
ωο- ω(0), and θ0-θ(0).
My Example: derive w2 - wo? = 2a(0-0).
dw
dw de
dw
a =
dt
de dt
de
Multiply by dt and integrate:
Sado
w dw = w?
d0 = a0 + C =
w?
2a0 + 2C
Substitute the initial (t=0) quantities, and subtract. The constant of
integration vanishes.
w3 = 2a0 + 2C
w? – w = 2a(0 – 0o)
The e integration fails if a is non-constant. There is also a type of
situation where the step before the integration fails, involving w.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7806ee1d-f52a-4446-9522-de19f1bf9bfb%2Ff9cedc7a-1e27-4e58-89c1-c539f35dd1c0%2Ffipu4uo_processed.jpeg&w=3840&q=75)
![Question 2: derive 0 = 1/2at² + wot
+ 0o-
You may use prior derived results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7806ee1d-f52a-4446-9522-de19f1bf9bfb%2Ff9cedc7a-1e27-4e58-89c1-c539f35dd1c0%2Frvkq5rb_processed.jpeg&w=3840&q=75)
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