Given that the position of a particle is defined in terms of time by the equation below, where x is in meters and t is in seconds, determine: 4t3 + t? 3t2 ++4 (a) the average velocity of the particle from t = 1.0 s to t = 3,0 s, (Ans: vave = 16 m/s) (b) the instantaneous velocity of the particle at t = 2.5 s, (Ans: B = 20.52 m/s) (c) the average acceleration of the particle from t = 2.0 s tot = 3.0 s, and (Ans: aave = 8.42 m/s³) (d) the t at which the instantaneous acceleration of particle is 8.10 m/s. (Ans: t = 3.91 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.
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