The position of a particle moving along an x axis is given by x = 202²-62³, where x is in meters and t is in seconds. Determine the position of the particle at t = 3.0 s. 18 (b) Determine the velocity of the particle at t = 3.0 s. (Indicate the direction with the sign of your answer.) 42 m/s -42 (c) Determine the acceleration of the particle at t = 3.0 s. (Indicate the direction with the sign of your answer.) -68 -68 m/s² (d) What is the maximum positive coordinate reached by the particle? 32.9218 32.9 m (e) At what time is it reached? 2.222 2.22 S (f) What is the maximum positive velocity reached by the particle? 22.222 22.2 m/s (9) At what time is it reached? 1.111✔ 1.11 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.) -39.9992 40 m/s² Determine the average velocity of the particle between t= 0 and t = 3 s. (Indicate the direction with the sign of your answer.) 6 m/s Additional Materials Derivative of a Polynomial
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 = 201²- 62³, where x is in meters and t is in seconds.
Determine the position of the particle at t = 3.0 s.
18 m
18
(b) Determine the velocity of the particle at t = 3.0 s. (Indicate the direction with the sign of your answer.)
-42 m/s
(c) Determine the acceleration of the particle at t = 3.0 s. (Indicate the direction with the sign of your answer.)
-68
-68 m/s2
(d) What is the maximum positive coordinate reached by the particle?
32.9218
32.9 m
(e) At what time is it reached?
2.222
2.22 S
(f) What is the maximum positive velocity reached by the particle?
22.222
22.2 m/s
(g) At what time is it reached?
1.111
1.11 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.)
-39.9992
40 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.)
6 m/s
Additional Materials
• Derivative of a Polynomial](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee22cf2f-b974-4b00-a3cf-09b388e7d65d%2Fe41056de-4d90-48e1-a61d-7d799fccf48e%2F7xyy8ld_processed.jpeg&w=3840&q=75)
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