The position of a particle for t > 0 is given by r(t) = (9.0t²i – 5.0e³j – 9.0t-2k) m. (a) What is the velocity as a function of time? (Express your answer in vector form. Use the following as necessary: t. Assume t is in seconds and v is in m/s. Do not include units in your answer.) v(t) = (b) What is the acceleration as a function of time? (Express your answer in vector form. Use the following as necessary: t. Assume t is in seconds and a is in m/s?. Do not include units in your answer.) a(t) = (c) What is the particle's velocity at t = 2.0 s (in m/s)? (Express your answer in vector form.) v(2.0 s) = m/s (d) What is its speed at t = 1.0 s and t = 3.0 s (in m/s)? v(1.0 s) = m/s v(3.0 s) = m/s (e) What is the average velocity between t = 1.0 s and t = 2.0 s (in m/s)? (Express your answer in vector form.) Vavg m/s

The position of a particle for t > 0 is given by r(t) = (9.0t²i – 5.0e³j – 9.0t-2k) m. (a) What is the velocity as a function of time? (Express your answer in vector form. Use the following as necessary: t. Assume t is in seconds and v is in m/s. Do not include units in your answer.) v(t) = (b) What is the acceleration as a function of time? (Express your answer in vector form. Use the following as necessary: t. Assume t is in seconds and a is in m/s?. Do not include units in your answer.) a(t) = (c) What is the particle's velocity at t = 2.0 s (in m/s)? (Express your answer in vector form.) v(2.0 s) = m/s (d) What is its speed at t = 1.0 s and t = 3.0 s (in m/s)? v(1.0 s) = m/s v(3.0 s) = m/s (e) What is the average velocity between t = 1.0 s and t = 2.0 s (in m/s)? (Express your answer in vector form.) Vavg m/s

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Description: The position of a particle for t > 0 is given by r(t) = (9.0t²î – 5.0t³j – 9.0t-2k) m.(a) What is the velocity as a function of time? (Express your answer in vector form. Use the following as necessary: t. Assume t is in seconds and v is in m/s. Do

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

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.

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Question

The position of a particle for t > 0 is given by r(t) = (9.0t²î – 5.0t³j – 9.0t-2k) m.
(a) What is the velocity as a function of time? (Express your answer in vector form. Use the following as necessary: t. Assume t is in seconds and v is in m/s. Do not include units in your answer.)
v(t) =
(b) What is the acceleration as a function of time? (Express your answer in vector form. Use the following as necessary: t. Assume t is in seconds and a is in m/s. Do not include units in your
answer.)
a(t)
%3D
(c) What is the particle's velocity at t = 2.0 s (in m/s)? (Express your answer in vector form.)
v(2.0 s) =
m/s
(d) What is its speed att = 1.0 s and t = 3.0 s (in m/s)?
v(1.0 s) =
m/s
v(3.0 s)
m/s
%D
(e) What is the average velocity between t = 1.0 s and t = 2.0 s (in m/s)? (Express your answer in vector form.)
m/s
avg

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