(d) When is the particle speeding up? Slowing down? Speeding up: 0 < t < 10 ▼ Slowing down: 0 < t < 10 (e) Find the total distance traveled by the particle from time t = 0 to time t - 12. The total distance = 180 ft
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 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) = t³ - 15t², t≥0
(a) Find the velocity and acceleration functions.
v(t) = 3 t² - 30 t
a(t) = 6 t - 30
(b) Find the position, velocity, speed, and acceleration at time t = 2.
s(2):
Speed=
-
-52
48
ft
ft/s
v(2) =
a(2) =
48
18
ft/s
ft/s²
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7bfc12f-449e-4627-9f8e-a2aee8e31590%2F4cdd4ae6-d96a-4f82-b177-84d78cf53ea2%2F6kd56s_processed.jpeg&w=3840&q=75)
![(c) At what times is the particle stopped?
Number of times the particle stopped:
0
(d) When is the particle speeding up? Slowing down?
Speeding up: 0<t< 10 ▼
Slowing down: 0 < t < 10
(e) Find the total distance traveled by the particle
from time t = 0 to time t = 12.
The total distance
=
180
ft
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7bfc12f-449e-4627-9f8e-a2aee8e31590%2F4cdd4ae6-d96a-4f82-b177-84d78cf53ea2%2F7t1edb4_processed.jpeg&w=3840&q=75)
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