Difference between revisions of "009B Sample Midterm 2, Problem 3"

From Grad Wiki
Jump to navigation Jump to search
Line 10: Line 10:
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Foundations:    
 
!Foundations:    
 +
|-
 +
|'''1.''' How are the velocity function <math>v(t)</math> and the position function <math>s(t)</math> related?
 
|-
 
|-
 
|
 
|
 +
::They are related by the equation <math>v(t)=s'(t).</math>
 +
|-
 +
|'''2.''' If we calculate <math>\int_a^b v(t)~dt,</math> what are we calculating?
 
|-
 
|-
 
|
 
|
 +
::We are calculating <math>s(b)-s(a).</math> This is the displacement of the particle from <math>t=a</math> to <math>t=b.</math>
 +
|-
 +
|'''3.''' If we calculate <math>\int_a^b |v(t)|~dt,</math> what are we calculating?
 
|-
 
|-
 
|
 
|
 +
::We are calculating the total distance traveled by the particle from <math>t=a</math> to <math>t=b.</math>
 
|}
 
|}
  

Revision as of 19:19, 6 February 2017

A particle moves along a straight line with velocity given by:

feet per second. Determine the total distance traveled by the particle

from time Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t=0} to time Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t=10.}


Foundations:  
1. How are the velocity function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v(t)} and the position function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle s(t)} related?
They are related by the equation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v(t)=s'(t).}
2. If we calculate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_a^b v(t)~dt,} what are we calculating?
We are calculating Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle s(b)-s(a).} This is the displacement of the particle from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t=a} to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t=b.}
3. If we calculate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_a^b |v(t)|~dt,} what are we calculating?
We are calculating the total distance traveled by the particle from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t=a} to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t=b.}


Solution:

Step 1:  
Step 2:  


Final Answer:  

Return to Sample Exam

Retrieved from "https://gradwiki.math.ucr.edu/index.php?title=009B_Sample_Midterm_2,_Problem_3&oldid=2019"