The position vs. time graph for an object traveling in one dimension is shown below: x [m] -1 -2 -3 1 2 3 4 5 6 7 t [s] = 4s to t = From t = 0s to t = 2s, position is given by x = -0.5t² +t; from t = 2s to t = 4s, position is given by x = 2-t; and from t = 8s, position is given by x = 0.25t² - 3t+6. (a) Draw a set of three stacked graphs describing this motion, i.e. reproduce the x(t) graph, below it draw vz(t), and below that draw ar(t). For each graph, be sure to write the appropriate equations describing the curve, in addition to drawing the curve. Make each graph as quantitatively precise as possible. (b) Over which time interval(s) is velocity constant? (c) Over which time interval(s) is acceleration constant?
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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![The position vs. time graph for an object traveling in one dimension is shown below:
x [m]
1
-1
-2
-3
N
4
5
7
-
From t = Os to t = 2s, position is given by x = -0.5t² +t; from t = 2s to t = 4s, position
is given by x = 2-t; and from t 4s to t 8s, position is given by x = 0.25t² - 3t+6.
(a) Draw a set of three stacked graphs describing this motion, i.e. reproduce the x(t)
graph, below it draw v(t), and below that draw ax(t). For each graph, be sure
to write the appropriate equations describing the curve, in addition to drawing the
curve. Make each graph as quantitatively precise as possible.
(b) Over which time interval(s) is velocity constant?
(c) Over which time interval(s) is acceleration constant?
(d) At what time(s) does the object turn around, or change the direction in which it
is moving (in other words, what are its turning points)? What is velocity at these
time(s)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4143f45a-5c96-4449-af2f-abda697f3e91%2Fd0c7ac87-1f4f-4f38-9b7d-bcb0f6cd5cd0%2F77mq20d_processed.jpeg&w=3840&q=75)
Given that,
Between the time-interval 0 to 2 s, the position is
Between the time-interval 2 s to 4 s, the position is
Between the time-interval 4 s to 8 s, the position is
Since velocity is
And acceleration
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