The position of a particle moving along an x-axis is given by x = 20t2 − 3t3, where x is in meters and t is in seconds. (a) Determine the position of the particle at t = 3.0 s. -----m (b) Determine the velocity of the particle at t = 3.0 s. (Indicate the direction with the sign of your answer.) -----m/s (c) Determine the acceleration of the particle at t = 3.0 s. (Indicate the direction with the sign of your answer.) -----m/s2
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 an x-axis is given by x = 20t2 − 3t3, where x is in meters and t is in seconds.
-----m
(b) Determine the velocity of the particle at t = 3.0 s. (Indicate the direction with the sign of your answer.)
-----m/s
(c) Determine the acceleration of the particle at t = 3.0 s. (Indicate the direction with the sign of your answer.)
-----m/s2
(d) What is the maximum positive coordinate reached by the particle?
-----m
(e) At what time is it reached?
-----s
(f) What is the maximum positive velocity reached by the particle?
-----m/s
(g) At what time is it reached?
-----s
(h) What is the acceleration of the particle at the instant the particle is not moving (other than at t = 0)? (Indicate the direction with the sign of your answer.)
-----m/s2
(i) Determine the average velocity of the particle between t = 0 and t = 3 s. (Indicate the direction with the sign of your answer.)
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