The velocity of a particle constrained to move along the x-axis as a function of timetis given by: Part A v(t)=-(19/to)sin(t/to). If the particle is at x=7 m when t = 0, what is its position at t = 6to- You will not need the value of to to solve any part of this problem. If it is bothering you, feel free to set to = 1 everywhere. Express your answer to 3 significant figures. • View Available Hint(s) ? m Submit Part B Denote instantaneous acceleration of this particle by a(t). Evaluate the expression 7 +v(0)t + a(0)t?/2 att = 6tg. Note that v(0) and a(0) are the velocity and acceleration at time t = 0. Express your answer to 3 significant figures. • View Available Hint(s) m
The velocity of a particle constrained to move along the x-axis as a function of timetis given by: Part A v(t)=-(19/to)sin(t/to). If the particle is at x=7 m when t = 0, what is its position at t = 6to- You will not need the value of to to solve any part of this problem. If it is bothering you, feel free to set to = 1 everywhere. Express your answer to 3 significant figures. • View Available Hint(s) ? m Submit Part B Denote instantaneous acceleration of this particle by a(t). Evaluate the expression 7 +v(0)t + a(0)t?/2 att = 6tg. Note that v(0) and a(0) are the velocity and acceleration at time t = 0. Express your answer to 3 significant figures. • View Available Hint(s) m
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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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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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
Answer parts A and B
![**Velocity of a Particle**
The velocity \( v(t) \) of a particle constrained to move along the x-axis as a function of time \( t \) is given by:
\[ v(t) = -\left(\frac{19}{t_0}\right)\sin\left(\frac{t}{t_0}\right) \]
**Part A**
- **Question:** If the particle is at \( x = 7 \, \text{m} \) when \( t = 0 \), what is its position at \( t = 6t_0 \)? You will not need the value of \( t_0 \) to solve any part of this problem. If it is bothering you, feel free to set \( t_0 = 1 \) everywhere.
- **Instruction:** Express your answer to 3 significant figures.
- **Input Field:**
- An input box is provided for entering the answer, followed by "m", indicating the unit is meters.
- A 'Submit' button is available for submission of the answer.
**Part B**
- **Question:** Denote instantaneous acceleration of this particle by \( a(t) \). Evaluate the expression \( 7 + v(0)t + a(0)t^2/2 \) at \( t = 6t_0 \). Note that \( v(0) \) and \( a(0) \) are the velocity and acceleration at time \( t = 0 \).
- **Instruction:** Express your answer to 3 significant figures.
- **Input Field:**
- An input box is provided for entering the answer, followed by "m", indicating the unit is meters.
- A 'Submit' button is available for submission of the answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ff1c888-964e-4444-aacc-2152d4151491%2Ff080ae62-1eec-49b0-8881-14fe1c955da7%2Fswgwuk_processed.png&w=3840&q=75)
Transcribed Image Text:**Velocity of a Particle**
The velocity \( v(t) \) of a particle constrained to move along the x-axis as a function of time \( t \) is given by:
\[ v(t) = -\left(\frac{19}{t_0}\right)\sin\left(\frac{t}{t_0}\right) \]
**Part A**
- **Question:** If the particle is at \( x = 7 \, \text{m} \) when \( t = 0 \), what is its position at \( t = 6t_0 \)? You will not need the value of \( t_0 \) to solve any part of this problem. If it is bothering you, feel free to set \( t_0 = 1 \) everywhere.
- **Instruction:** Express your answer to 3 significant figures.
- **Input Field:**
- An input box is provided for entering the answer, followed by "m", indicating the unit is meters.
- A 'Submit' button is available for submission of the answer.
**Part B**
- **Question:** Denote instantaneous acceleration of this particle by \( a(t) \). Evaluate the expression \( 7 + v(0)t + a(0)t^2/2 \) at \( t = 6t_0 \). Note that \( v(0) \) and \( a(0) \) are the velocity and acceleration at time \( t = 0 \).
- **Instruction:** Express your answer to 3 significant figures.
- **Input Field:**
- An input box is provided for entering the answer, followed by "m", indicating the unit is meters.
- A 'Submit' button is available for submission of the answer.
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