A particle moves according to a law of motion s = f(t) = t³ - 15t² + 72t, t≥ 0, where t is measured in seconds and s in feet. (a) Find the velocity at time t. v(t) = 31²-30t+72 ft/s (b) What is the velocity after 5 s? v(5) = -3 ft/s (c) When is the particle at rest? t = 4 t = 6 s (smaller value) s (larger value)
A particle moves according to a law of motion s = f(t) = t³ - 15t² + 72t, t≥ 0, where t is measured in seconds and s in feet. (a) Find the velocity at time t. v(t) = 31²-30t+72 ft/s (b) What is the velocity after 5 s? v(5) = -3 ft/s (c) When is the particle at rest? t = 4 t = 6 s (smaller value) s (larger value)
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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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![### Problem Statement
A particle moves according to a law of motion \( s = f(t) = t^3 - 15t^2 + 72t \), where \( t \geq 0 \), \( t \) is measured in seconds, and \( s \) is in feet.
### Questions and Solutions
#### (a) Find the velocity at time \( t \).
**Solution**:
\[ v(t) = 3t^2 - 30t + 72 \quad \text{ft/s} \]
*(Correct)*
#### (b) What is the velocity after 5 seconds?
**Solution**:
\[ v(5) = -3 \quad \text{ft/s} \]
*(Correct)*
#### (c) When is the particle at rest?
**Solution**:
\[ t = 4 \quad s \quad \text{(smaller value)} \]
\[ t = 6 \quad s \quad \text{(larger value)} \]
*(Correct)*
#### (d) When is the particle moving in the positive direction?
**Response Required**:
\[
( \, \underline{\hspace{2cm}} \, , \, \underline{\hspace{2cm}} \, ) \cup ( \, \underline{\hspace{2cm}} \, , \, \underline{\hspace{2cm}} \, )
\]
*(Incorrect)*
#### (e) Find the total distance traveled during the first 9 seconds.
**Response Required**:
\[ \underline{\hspace{4cm}} \quad \text{feet} \]
*(Incorrect)*
#### (f) Draw a diagram to illustrate the motion of the particle.
**Instruction**: Do this on paper. Your instructor may ask you to turn in this graph.
#### (g) Find the acceleration at time \( t \) and after 5 seconds.
**Response Required**:
\[ a(t) = \underline{\hspace{4cm}} \]
\[ a(5) = \underline{\hspace{4cm}} \quad \text{ft/s}^2 \]
*(Incorrect)*
#### (h) Graph the position, velocity, and acceleration functions for \( 0 \leq t \leq 9 \).
**Instruction**: Do this on paper. Your](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F009b160c-b3fb-420f-ae32-098cf06f011d%2F9c19f410-6c5e-4754-8921-d6dfcab1d5ae%2F8ph23ep_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A particle moves according to a law of motion \( s = f(t) = t^3 - 15t^2 + 72t \), where \( t \geq 0 \), \( t \) is measured in seconds, and \( s \) is in feet.
### Questions and Solutions
#### (a) Find the velocity at time \( t \).
**Solution**:
\[ v(t) = 3t^2 - 30t + 72 \quad \text{ft/s} \]
*(Correct)*
#### (b) What is the velocity after 5 seconds?
**Solution**:
\[ v(5) = -3 \quad \text{ft/s} \]
*(Correct)*
#### (c) When is the particle at rest?
**Solution**:
\[ t = 4 \quad s \quad \text{(smaller value)} \]
\[ t = 6 \quad s \quad \text{(larger value)} \]
*(Correct)*
#### (d) When is the particle moving in the positive direction?
**Response Required**:
\[
( \, \underline{\hspace{2cm}} \, , \, \underline{\hspace{2cm}} \, ) \cup ( \, \underline{\hspace{2cm}} \, , \, \underline{\hspace{2cm}} \, )
\]
*(Incorrect)*
#### (e) Find the total distance traveled during the first 9 seconds.
**Response Required**:
\[ \underline{\hspace{4cm}} \quad \text{feet} \]
*(Incorrect)*
#### (f) Draw a diagram to illustrate the motion of the particle.
**Instruction**: Do this on paper. Your instructor may ask you to turn in this graph.
#### (g) Find the acceleration at time \( t \) and after 5 seconds.
**Response Required**:
\[ a(t) = \underline{\hspace{4cm}} \]
\[ a(5) = \underline{\hspace{4cm}} \quad \text{ft/s}^2 \]
*(Incorrect)*
#### (h) Graph the position, velocity, and acceleration functions for \( 0 \leq t \leq 9 \).
**Instruction**: Do this on paper. Your
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