A particle moves only along the x axis. Its position varies with time according to the equation x = -6t + 2t^2, where x is in meters and t is in seconds. a) Graph its position, velocity, and acceleration, as a function of time, in the interval 0 ≤ t ≤ 4 s. (Use a table for t = 0, 1, 2, 3, 4 s to construct the graphs). b) In what time interval does it move to the left and in which time interval does it move to the right? c) Calculate the instantaneous velocity and acceleration at t = 1.5 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.
A particle moves only along the x axis. Its position varies with time according to the equation x = -6t + 2t^2, where x is in meters and t is in seconds. a) Graph its position, velocity, and acceleration, as a function of time, in the interval 0 ≤ t ≤ 4 s. (Use a table for t = 0, 1, 2, 3, 4 s to construct the graphs). b) In what time interval does it move to the left and in which time interval does it move to the right? c) Calculate the instantaneous velocity and acceleration at t = 1.5 s.
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