The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds. s(1) = 912 – 271, t>0 (a) Find the velocity and acceleration functions. v(t): a(t): (b) Over what interval is the particle moving in the positive direction? Use inf to represent oo. Interval: (c) Over what interval is the particle moving in the negative direction? Use inf to represent oo. Interval: (d) Over what interval is the particle speeding up? Slowing down? Use inf to represent co. Speeding up: Slowing down: Note: You can earn partial credit on this problem.
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.
![E The function s(t) describes the position
of a particle moving along a coordinate line,
where s is in feet and t is in seconds.
s(t) = 9t2 – 27t,
t > 0
(a) Find the velocity and acceleration functions.
v(t):
a(t):
(b) Over what interval is the particle moving in
the positive direction? Use inf to represent o.
Interval:
(c) Over what interval is the particle moving in
the negative direction? Use inf to represent oo.
Interval:
(d) Over what interval is the particle speeding
up? Slowing down? Use inf to represent co.
Speeding up:
Slowing down:
Note: You can earn partial credit on this
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