009B Sample Midterm 2, Problem 3 - Revision history

Kayla Murray at 20:40, 14 March 2017

2017-03-14T20:40:24Z

Kayla Murray at 01:26, 27 February 2017

2017-02-27T01:26:44Z

Kayla Murray at 00:12, 19 February 2017

2017-02-19T00:12:47Z

Kayla Murray at 01:55, 8 February 2017

2017-02-08T01:55:58Z

Kayla Murray at 16:45, 7 February 2017

2017-02-07T16:45:20Z

Kayla Murray at 15:02, 7 February 2017

2017-02-07T15:02:59Z

Kayla Murray at 04:32, 7 February 2017

2017-02-07T04:32:15Z

Kayla Murray at 04:26, 7 February 2017

2017-02-07T04:26:59Z

Kayla Murray at 04:12, 7 February 2017

2017-02-07T04:12:06Z

Kayla Murray at 04:03, 7 February 2017

2017-02-07T04:03:00Z

@@ Line 48: / Line 48: @@
 |We need to figure out when &nbsp;<math style="vertical-align: -2px">-32t+200</math>&nbsp; is positive and negative in the interval &nbsp;<math style="vertical-align: -6px">[0,10].</math>
 |-
-|We set &nbsp;<math style="vertical-align: -2px">-32t+200=0</math>&nbsp; and solve for &nbsp;<math style="vertical-align: -1px">t.</math>
+|We set
 |-
-|We get &nbsp;<math style="vertical-align: -1px">t=6.25.</math>
+|&nbsp; &nbsp; &nbsp; &nbsp;<math style="vertical-align: -2px">-32t+200=0</math>
 |-
 |Then, we use test points to see that &nbsp;<math style="vertical-align: -2px">-32t+200</math>&nbsp; is positive from &nbsp;<math style="vertical-align: -6px">[0,6.25]</math>

@@ Line 5: / Line 5: @@
 <span class="exam">feet per second. Determine the total distance traveled by the particle
-<span class="exam">from time <math style="vertical-align: 0px">t=0</math> to time <math style="vertical-align: -1px">t=10.</math>
+<span class="exam">from time &nbsp;<math style="vertical-align: 0px">t=0</math>&nbsp; to time &nbsp;<math style="vertical-align: -1px">t=10.</math>
@@ Line 11: / Line 11: @@
 !Foundations: &nbsp;
 |-
-|'''1.''' How are the velocity function <math style="vertical-align: -5px">v(t)</math> and the position function <math style="vertical-align: -5px">s(t)</math> related?
+|'''1.''' How are the velocity function &nbsp;<math style="vertical-align: -5px">v(t)</math>&nbsp; and the position function &nbsp;<math style="vertical-align: -5px">s(t)</math>&nbsp; related?
 |-
+|
-&nbsp; &nbsp; &nbsp; &nbsp; They are related by the equation <math style="vertical-align: -5px">v(t)=s'(t).</math>
+&nbsp; &nbsp; &nbsp; &nbsp; They are related by the equation &nbsp;<math style="vertical-align: -5px">v(t)=s'(t).</math>
 |-
-|'''2.''' If we calculate <math style="vertical-align: -14px">\int_a^b v(t)~dt,</math> what are we calculating?
+|'''2.''' If we calculate &nbsp;<math style="vertical-align: -14px">\int_a^b v(t)~dt,</math>&nbsp; what are we calculating?
 |-
+|
-&nbsp; &nbsp; &nbsp; &nbsp; We are calculating <math style="vertical-align: -5px">s(b)-s(a).</math>
+&nbsp; &nbsp; &nbsp; &nbsp; We are calculating &nbsp;<math style="vertical-align: -5px">s(b)-s(a).</math>
 |-
+|
-&nbsp; &nbsp; &nbsp; &nbsp; This is the displacement of the particle from <math style="vertical-align: 0px">t=a</math> to <math style="vertical-align: 0px">t=b.</math>
+&nbsp; &nbsp; &nbsp; &nbsp; This is the displacement of the particle from &nbsp;<math style="vertical-align: 0px">t=a</math>&nbsp; to &nbsp;<math style="vertical-align: 0px">t=b.</math>
 |-
-|'''3.''' If we calculate <math style="vertical-align: -14px">\int_a^b |v(t)|~dt,</math> what are we calculating?
+|'''3.''' If we calculate &nbsp;<math style="vertical-align: -14px">\int_a^b |v(t)|~dt,</math>&nbsp; what are we calculating?
 |-
+|
-&nbsp; &nbsp; &nbsp; &nbsp; We are calculating the total distance traveled by the particle from <math style="vertical-align: 0px">t=a</math> to <math style="vertical-align: 0px">t=b.</math>
+&nbsp; &nbsp; &nbsp; &nbsp; We are calculating the total distance traveled by the particle from &nbsp;<math style="vertical-align: 0px">t=a</math>&nbsp; to &nbsp;<math style="vertical-align: 0px">t=b.</math>
 |}
@@ Line 36: / Line 36: @@
 !Step 1: &nbsp;
 |-
-|To calculate the total distance the particle traveled from <math style="vertical-align: -1px">t=0</math> to <math style="vertical-align: -5px">t=10,</math>
+|To calculate the total distance the particle traveled from &nbsp;<math style="vertical-align: -1px">t=0</math>&nbsp; to &nbsp;<math style="vertical-align: -5px">t=10,</math>
 |-
 |we need to calculate
@@ Line 46: / Line 46: @@
 !Step 2: &nbsp;
 |-
-|We need to figure out when <math style="vertical-align: -2px">-32t+200</math> is positive and negative in the interval <math style="vertical-align: -6px">[0,10].</math>
+|We need to figure out when &nbsp;<math style="vertical-align: -2px">-32t+200</math>&nbsp; is positive and negative in the interval &nbsp;<math style="vertical-align: -6px">[0,10].</math>
 |-
-|We set <math style="vertical-align: -2px">-32t+200=0</math> and solve for <math style="vertical-align: -1px">t.</math>
+|We set &nbsp;<math style="vertical-align: -2px">-32t+200=0</math>&nbsp; and solve for &nbsp;<math style="vertical-align: -1px">t.</math>
 |-
-|We get <math style="vertical-align: -1px">t=6.25.</math>
+|We get &nbsp;<math style="vertical-align: -1px">t=6.25.</math>
 |-
-|Then, we use test points to see that <math style="vertical-align: -2px">-32t+200</math> is positive from <math style="vertical-align: -6px">[0,6.25]</math>
+|Then, we use test points to see that &nbsp;<math style="vertical-align: -2px">-32t+200</math>&nbsp; is positive from &nbsp;<math style="vertical-align: -6px">[0,6.25]</math>
 |-
-|and negative from <math>[6.25,10].</math>
+|and negative from &nbsp;<math>[6.25,10].</math>
 |}
@@ Line 78: / Line 78: @@
 !Final Answer: &nbsp;
 |-
-|&nbsp; &nbsp; &nbsp; &nbsp; The particle travels <math style="vertical-align: -1px">850</math> feet.
+|&nbsp; &nbsp; &nbsp; &nbsp; The particle travels &nbsp;<math style="vertical-align: -1px">850</math> &nbsp; feet.
 |}
 [[009B_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]

@@ Line 1: / Line 1: @@
 <span class="exam"> A particle moves along a straight line with velocity given by:
-::::::<math>v(t)=-32t+200</math>
+::<math>v(t)=-32t+200</math>
 <span class="exam">feet per second. Determine the total distance traveled by the particle

@@ Line 14: / Line 14: @@
 |-
+|
-&nbsp; &nbsp; They are related by the equation <math style="vertical-align: -5px">v(t)=s'(t).</math>
+&nbsp; &nbsp; &nbsp; &nbsp; They are related by the equation <math style="vertical-align: -5px">v(t)=s'(t).</math>
 |-
 |'''2.''' If we calculate <math style="vertical-align: -14px">\int_a^b v(t)~dt,</math> what are we calculating?
 |-
+|
-&nbsp; &nbsp; We are calculating <math style="vertical-align: -5px">s(b)-s(a).</math>
+&nbsp; &nbsp; &nbsp; &nbsp; We are calculating <math style="vertical-align: -5px">s(b)-s(a).</math>
 |-
+|
-&nbsp; &nbsp; This is the displacement of the particle from <math style="vertical-align: 0px">t=a</math> to <math style="vertical-align: 0px">t=b.</math>
+&nbsp; &nbsp; &nbsp; &nbsp; This is the displacement of the particle from <math style="vertical-align: 0px">t=a</math> to <math style="vertical-align: 0px">t=b.</math>
 |-
 |'''3.''' If we calculate <math style="vertical-align: -14px">\int_a^b |v(t)|~dt,</math> what are we calculating?
 |-
+|
-&nbsp; &nbsp; We are calculating the total distance traveled by the particle from <math style="vertical-align: 0px">t=a</math> to <math style="vertical-align: 0px">t=b.</math>
+&nbsp; &nbsp; &nbsp; &nbsp; We are calculating the total distance traveled by the particle from <math style="vertical-align: 0px">t=a</math> to <math style="vertical-align: 0px">t=b.</math>
 |}
@@ Line 36: / Line 36: @@
 !Step 1: &nbsp;
 |-
-|To calculate the total distance the particle traveled from <math style="vertical-align: -1px">t=0</math> to <math style="vertical-align: -5px">t=10,</math> we need to calculate
+|To calculate the total distance the particle traveled from <math style="vertical-align: -1px">t=0</math> to <math style="vertical-align: -5px">t=10,</math>
 |-
-|&nbsp; &nbsp; <math>\int_0^{10} |v(t)|~dt=\int_0^{10} |-32t+200|~dt.</math>
+|we need to calculate
 |}
@@ Line 61: / Line 63: @@
 |-
+|
-&nbsp; &nbsp; <math>\begin{array}{rcl}
+&nbsp; &nbsp; &nbsp; &nbsp; <math>\begin{array}{rcl}
 \displaystyle{\int_0^{10} |-32t+200|~dt} & = & \displaystyle{\int_0^{6.25} -32t+200~dt+\int_{6.25}^{10}-(-32t+200)~dt}\\
 &&\\
@@ Line 76: / Line 78: @@
 !Final Answer: &nbsp;
 |-
-|The particle travels <math style="vertical-align: -1px">850</math> feet.
+|&nbsp; &nbsp; &nbsp; &nbsp; The particle travels <math style="vertical-align: -1px">850</math> feet.
 |}
 [[009B_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]

@@ Line 14: / Line 14: @@
 |-
+|
-::They are related by the equation <math style="vertical-align: -5px">v(t)=s'(t).</math>
+&nbsp; &nbsp; They are related by the equation <math style="vertical-align: -5px">v(t)=s'(t).</math>
 |-
 |'''2.''' If we calculate <math style="vertical-align: -14px">\int_a^b v(t)~dt,</math> what are we calculating?
 |-
+|
-::We are calculating <math style="vertical-align: -5px">s(b)-s(a).</math>
+&nbsp; &nbsp; We are calculating <math style="vertical-align: -5px">s(b)-s(a).</math>
 |-
+|
-::This is the displacement of the particle from <math style="vertical-align: 0px">t=a</math> to <math style="vertical-align: 0px">t=b.</math>
+&nbsp; &nbsp; This is the displacement of the particle from <math style="vertical-align: 0px">t=a</math> to <math style="vertical-align: 0px">t=b.</math>
 |-
 |'''3.''' If we calculate <math style="vertical-align: -14px">\int_a^b |v(t)|~dt,</math> what are we calculating?
 |-
+|
-::We are calculating the total distance traveled by the particle from <math style="vertical-align: 0px">t=a</math> to <math style="vertical-align: 0px">t=b.</math>
+&nbsp; &nbsp; We are calculating the total distance traveled by the particle from <math style="vertical-align: 0px">t=a</math> to <math style="vertical-align: 0px">t=b.</math>
 |}