A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = 0.01t4 − 0.03t3 (a) Find the velocity at time t (in ft/s). v(t) = (b) What is the velocity after 1 second(s)? v(1) = ft/s (c) When is the particle at rest? t = s (smaller value) t = s (larger value)
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.
A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet.
v(t) =
(b) What is the velocity after 1 second(s)?
v(1) = ft/s
(c) When is the particle at rest?
| t = s (smaller value) |
| t = s (larger value) |
(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)
ft
(f) Find the acceleration at time t (in ft/s2).
Find the acceleration after 1 second(s).
(g) Graph the position, velocity, and acceleration functions for the first 11 seconds.
(h) When, for
When, for
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