The position of a particle moving along the x axis depends on the time according to the equation x = ct2 = bt3, where x is in meters and t in seconds.What are the units of (a) constant c and (b) constant b? Let their numerical values be 3.0 and 2.0, respectively. (c) At what time does the particle reach its maximum positive x position? From t = 0.0 s to t = 4.0 s, (d) what distance does the particle move and (e) what is its displacement? Find its velocity at times (f) 1.0 s, (g) 2.0 s, (h) 3.0 s, and (i) 4.0 s. Find its acceleration at times (j) 1.0 s, (k) 2.0 s, (l) 3.0 s, and (m) 4.0 s.
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 position of a particle moving along the x axis depends on
the time according to the equation x = ct2 = bt3, where x is in meters
and t in seconds.What are the units of (a) constant c and (b) constant
b? Let their numerical values be 3.0 and 2.0, respectively. (c) At
what time does the particle reach its maximum positive x position?
From t = 0.0 s to t = 4.0 s, (d) what distance does the particle move
and (e) what is its displacement? Find its velocity at times (f) 1.0 s,
(g) 2.0 s, (h) 3.0 s, and (i) 4.0 s. Find its acceleration at times (j) 1.0 s,
(k) 2.0 s, (l) 3.0 s, and (m) 4.0 s.
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