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Subject: Equations of Motion
Date: Wed, 29 Dec 2004 06:30:02 -0500
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<META content=3D"Klaus Oetjen" name=3DAuthor>
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<BODY text=3D#000000 vLink=3D#800080 aLink=3D#ff0000 link=3D#0000ff =
bgColor=3Dwhite>
<BLOCKQUOTE>
  <TABLE bgColor=3D#ffff00>
    <TBODY>
    <TR>
      <TD><B>Multiple Choice Test</B><BR>Indicate the correct answer by=20
        clicking on the button next to the numbers 1, 2, 3 or 4. There =
is only=20
        one correct answer per question. After you have answered=20
        <B><U>all</U></B> multiple choice questions compare your choices =
with=20
        the correct answers. </TD></TR></TBODY></TABLE>
  <HR width=3D"100%" color=3Dblue SIZE=3D3>

  <CENTER>
  <H2>Equations of Motion I</H2></CENTER>
  <HR width=3D"100%" color=3Dblue SIZE=3D3>

  <FORM name=3DF><!frage1><B>1.) A motorcycle accelerates from 10 m/s to =
25 m/s in=20
  5 seconds. What is the average acceleration of the bike? </B>
  <UL>
    <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
      <TBODY>
      <TR>
        <TD width=3D40><B>1</B><INPUT type=3Dradio value=3D1 =
name=3DQ1></TD>
        <TD><B>3 m/s<SUP>2</SUP></B></TD></TR>
      <TR>
        <TD width=3D40><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ1></TD>
        <TD><B>5 m/s<SUP>2</SUP></B></TD></TR>
      <TR>
        <TD width=3D40><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ1></TD>
        <TD><B>15 m/s<SUP>2</SUP></B></TD></TR>
      <TR>
        <TD width=3D40><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ1></TD>
        <TD><B>25 m/s<SUP>2</SUP></B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Option <b>1</b> since acceleration=3Dchange of =
velocity per time=3D15km/h divided by 5s=3D3m/s<sup>2</sup>")' =
type=3Dbutton value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage2><B>2.) A ball is thrown vertically into the air and =
when it=20
  returns after an interval of 2 seconds, it is caught. Which one of the =

  following statements is true if the acceleration due to gravity is 10=20
  m/s<SUP>2</SUP> and air resistance can be neglected: </B>
  <UL>
    <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
      <TBODY>
      <TR>
        <TD width=3D40><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ2></TD>
        <TD><B>The acceleration at the top of its flight is 10=20
          m/s<SUP>2</SUP>.</B></TD></TR>
      <TR>
        <TD width=3D40><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ2></TD>
        <TD><B>The time taken for the descending motion does not equal =
the=20
          time taken for the ascending motion.</B> </TD></TR>
      <TR>
        <TD width=3D40><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ2></TD>
        <TD><B>The maximum height it reaches does not depend on the =
force of=20
          gravity.</B></TD></TR>
      <TR>
        <TD width=3D40><B>4</B><INPUT type=3Dradio value=3D1 =
name=3DQ2></TD>
        <TD><B>The acceleration after it leaves the hand is 10 =
m/s<SUP>2</SUP>=20
          downwards.</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("This type of question shows up again and again. =
Remember: the moment an object is in the air the acceleration is 10 =
m/s<sup>2</sup>with direction down, towards centre of the Earth. This is =
a result of the fact that in falling bodies the horizontal and vertical =
components of motion are independent of each other.")' type=3Dbutton =
value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage3>
  <TABLE>
    <TBODY>
    <TR>
      <TD vAlign=3Dtop width=3D"65%"><B>3.) A ball is thrown vertically =
up from=20
        the top of a building and the graph to the right shows the =
variation of=20
        its velocity with time up to the 5th second. <BR>At the end of =
its=20
        journey (as shown by the graph) the ball is =85=20
        <UL>
          <TABLE cellSpacing=3D0 cols=3D2 border=3D0>
            <TBODY>
            <TR>
              <TD width=3D40><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ3></TD>
              <TD><B>back at its point of projection.</B></TD></TR>
            <TR>
              <TD width=3D40><B>2</B><INPUT type=3Dradio value=3D1 =
name=3DQ3></TD>
              <TD><B>25 m from the point of projection and moving=20
                downwards.</B></TD></TR>
            <TR>
              <TD width=3D40><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ3></TD>
              <TD><B>45 m from the point of projection and moving=20
                downwards.</B></TD></TR>
            <TR>
              <TD width=3D40><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ3></TD>
              <TD><B>25 m from the point of projection and moving=20
              upwards.</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("It is clear that options 1 and 4 do not make a =
lot of sense. But is it 2 or 3? This is a tricky question. You might =
tend to go for 3, arguing that since at the top of the motion of an =
object thrown vertiaclly up velocity is zero, hence distance covered in =
3 seconds is 45m (s=3D1/2gt<sup>2</sup>). However, the ball did start =
its journey with an <b>initial velocity</b> of 20 m/s up. Hence: s=3Dut =
+ 1/2gt<sup>2</sup>=3D -150 + 125 =3D (- direction down) 25m.")' =
type=3Dbutton value=3DExplanation>
          <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
           </UL></B></TD>
      <TD vAlign=3Dtop align=3Dmiddle width=3D"35%"><IMG height=3D203=20
        alt=3D"equations of motion diagram 1"=20
        src=3D"http://www.sec.org.za/tests/pmcemot1.gif" width=3D259=20
    border=3D1></TD></TR></TBODY></TABLE><!frage4>
  <TABLE>
    <TBODY>
    <TR>
      <TD vAlign=3Dtop width=3D"50%"><B>4.) Which of the given =
<I><BIG>velocity :=20
        time</BIG></I> graphs <BR>(see box below) <BR>matches the given=20
        <I><BIG>acceleration : time</BIG></I> graph which you see at the =
right?=20
        </B></TD>
      <TD vAlign=3Dcenter align=3Dmiddle width=3D"50%"><IMG height=3D140 =

        alt=3D"equations of motion diagram 2"=20
        src=3D"http://www.sec.org.za/tests/pmcemot2.gif" width=3D184=20
    border=3D1></TD></TR></TBODY></TABLE></B>
  <UL><IMG height=3D291 alt=3D"equations of motion diagram 3"=20
    src=3D"http://www.sec.org.za/tests/pmcemot3.gif" width=3D498 =
border=3D2>=20
    <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
      <TBODY>
      <TR>
        <TD width=3D40><B>1</B><INPUT type=3Dradio value=3D1 =
name=3DQ4></TD>
        <TD><B>A</B></TD></TR>
      <TR>
        <TD width=3D40><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ4></TD>
        <TD><B>B</B></TD></TR>
      <TR>
        <TD width=3D40><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ4></TD>
        <TD><B>C</B></TD></TR>
      <TR>
        <TD width=3D40><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ4></TD>
        <TD><B>D</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("The given graph represents a motion with a =
positive constant acceleration (=3Dincrease in velocity) and thereafter =
a constant negative acceleration (=3Ddecrease in velocity). So which =
graph shows a positive and negative acceleration? B and C are out since =
they represent a constant acceleration. In B the gradient is positive =
hence a positive acceleration, C shows a constantly slowing down motion. =
But is it A or B? First we look for a positive acceleration, which is =
only in A the case, followed by a deceleration. Again only A fulfils =
this criteria.")' type=3Dbutton value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage5><B>5.) A ball is thrown vertically upwards. If air =
resistance=20
  is ignored, the ball will move with constant =85 </B>
  <UL>
    <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
      <TBODY>
      <TR>
        <TD width=3D40><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ5></TD>
        <TD><B>velocity</B></TD></TR>
      <TR>
        <TD width=3D40><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ5></TD>
        <TD><B>momentum</B></TD></TR>
      <TR>
        <TD width=3D40><B>3</B><INPUT type=3Dradio value=3D1 =
name=3DQ5></TD>
        <TD><B>acceleration</B></TD></TR>
      <TR>
        <TD width=3D40><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ5></TD>
        <TD><B>potential energy</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Compare with question 2. Again the same =
szenario: if object is airborne the acceleration is <b>g</b>")' =
type=3Dbutton value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage6><B>6.) A ball is thrown vertically upwards. Ignore =
air=20
  resistance. Take the upward motion as positive. Which one of the =
following=20
  graphs represents the velocity of the ball as a function of time? =
</B><BR><BR>
  <UL><IMG height=3D303 alt=3D"equations of motion diagram 4"=20
    src=3D"http://www.sec.org.za/tests/pmcemot4.gif" width=3D529 =
border=3D2>=20
    <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
      <TBODY>
      <TR>
        <TD width=3D40><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ6></TD>
        <TD><B>A</B></TD></TR>
      <TR>
        <TD width=3D40><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ6></TD>
        <TD><B>B</B></TD></TR>
      <TR>
        <TD width=3D40><B>3</B><INPUT type=3Dradio value=3D1 =
name=3DQ6></TD>
        <TD><B>C</B></TD></TR>
      <TR>
        <TD width=3D40><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ6></TD>
        <TD><B>D</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Acceleration is -10m/s<sup>2</sup> hence we have =
to look for a graph which has a constant negative gradient. Only C does =
so.")' type=3Dbutton value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage7>
  <TABLE>
    <TBODY>
    <TR>
      <TD vAlign=3Dtop><B>7.) Two heavy metal spheres P and Q are =
simultaneously=20
        dropped from the same height as shown in the diagram to the =
right. The=20
        sphere P is much smaller than sphere Q. Ignore the effect of air =

        resistance. <BR>Which one of the following is the correct =
observation=20
        and possible reason for what happens? </B></TD>
      <TD vAlign=3Dtop align=3Dmiddle><IMG height=3D167=20
        alt=3D"equations of motion diagram 5"=20
        src=3D"http://www.sec.org.za/tests/pmcemot5.gif" width=3D259=20
    border=3D0></TD></TR></TBODY></TABLE>
  <UL>
    <TABLE cellSpacing=3D0 cols=3D3 cellPadding=3D1 width=3D"90%" =
border=3D0>
      <TBODY>
      <TR>
        <TD width=3D"10%"></TD>
        <TD align=3Dmiddle =
width=3D"45%"><B><BIG><U>observation</U></BIG></B></TD>
        <TD align=3Dmiddle width=3D"45%"><B><BIG><U>possible=20
        reason</U></BIG></B></TD></TR>
      <TR>
        <TD width=3D"10%"><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ7></TD>
        <TD width=3D"45%"><B>they reach the floor =
simultaneously</B></TD>
        <TD width=3D"45%"><B>gravitational forces are equal for both=20
        spheres</B></TD></TR>
      <TR>
        <TD width=3D40><B>2</B><INPUT type=3Dradio value=3D1 =
name=3DQ7></TD>
        <TD><B>they reach the floor simultaneously</B></TD>
        <TD width=3D"45%"><B>the gravitational acceleration is the same =
for=20
          both</B></TD></TR>
      <TR>
        <TD width=3D40><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ7></TD>
        <TD><B>P reaches the floor first</B></TD>
        <TD width=3D"45%"><B>smaller objects always fall 'faster' than =
bigger=20
          ones</B></TD></TR>
      <TR>
        <TD width=3D40><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ7></TD>
        <TD><B>Q reaches the floor first</B></TD>
        <TD width=3D"45%"><B>the earth's force of gravity is greater on =
the=20
          heavier object</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("For 1: correct observation but the conclusion =
goes astray. The gravitational forces (weights of spheres) are not =
equal. 3 and 4 are full of mis- and preconceptions regarding falling =
objects (see the document <i>Aristotle versus Galileo</i> which you will =
find under <b>teaching resources Physics</b> on this website). Provided =
frictional forces are not considered 2 says it all.")' type=3Dbutton =
value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage8>
  <TABLE>
    <TBODY>
    <TR>
      <TD vAlign=3Dtop><B>8.) A ball falls vertically from rest from a =
high=20
        cliff from point A as shown in the sketch. At point B the ball =
reaches=20
        its terminal velocity. While the ball is falling from B to C, =
its=20
        kinetic energy will ... </B>
        <UL>
          <TABLE cellSpacing=3D0 cols=3D2 width=3D240 border=3D0>
            <TBODY>
            <TR>
              <TD width=3D40><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ8></TD>
              <TD width=3D200><B>be zero</B></TD></TR>
            <TR>
              <TD width=3D40><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ8></TD>
              <TD width=3D200><B>increase</B></TD></TR>
            <TR>
              <TD width=3D40><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ8></TD>
              <TD width=3D200><B>decrease</B></TD></TR>
            <TR>
              <TD width=3D40><B>4</B><INPUT type=3Dradio value=3D1 =
name=3DQ8></TD>
              <TD width=3D200><B>remain =
constant</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Kinetic energy=3D1/2mv<sup>2</sup>. After a =
falling body has reached its terminal velocity the frictional forces due =
to air resistance are balanced by the acceleration due to gravity =
(remember: no resultant force, no acceleration). Hence no change in =
velocity/speed between B and C; which results in a constant kinetic =
energy after the ball has passed point B.")' type=3Dbutton =
value=3DExplanation>
          <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
           </UL></TD>
      <TD align=3Dmiddle><IMG height=3D294 alt=3D"equations of motion =
diagram 6"=20
        src=3D"http://www.sec.org.za/tests/pmcemot6.gif" width=3D396=20
    border=3D2></TD></TR></TBODY></TABLE><BR><!frage9><B>9.) A rock is =
thrown=20
  vertically upwards with a speed 'v' from the edge of a cliff. At the =
same=20
  moment, a second rock is thrown vertically downwards with the same =
initial=20
  speed 'v'. Which of the following statements regarding the motion of =
the rocks=20
  is true (ignore air resistance.)? </B>
  <UL>
    <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
      <TBODY>
      <TR>
        <TD width=3D40><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ9></TD>
        <TD><B>The rock which was thrown upwards reaches the bottom of =
the=20
          cliff with a higher velocity.</B></TD></TR>
      <TR>
        <TD width=3D40><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ9></TD>
        <TD><B>The rock which was thrown downwards reaches the bottom of =
the=20
          cliff with a higher velocity.</B></TD></TR>
      <TR>
        <TD width=3D40><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ9></TD>
        <TD><B>Both rocks reach the bottom of the cliff with the same =
velocity=20
          at the same time.</B></TD></TR>
      <TR>
        <TD width=3D40><B>4</B><INPUT type=3Dradio value=3D1 =
name=3DQ9></TD>
        <TD><B>Both rocks reach the bottom of the cliff with the same =
velocity=20
          but at different times.</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Option 4 is the good one. This is a dangerous =
question because in many similar sounding questions so often the objects =
hit the ground at the same time due to the same gravitational =
acceleration (see also question 7). But in this case the initial =
velocity of the stone which was dropped was not zero hence it will reach =
the ground first.")' type=3Dbutton value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL>
  <TABLE>
    <TBODY>
    <TR>
      <TD vAlign=3Dtop><B>10.) The path PQR of a soccer ball kicked from =
a point=20
        P on the ground is shown in the diagram at the right. At point =
Q, the=20
        ball is at its maximum height. <BR></B></TD>
      <TD vAlign=3Dtop><IMG height=3D108 alt=3D"equations of motion =
diagram 7a"=20
        src=3D"http://www.sec.org.za/tests/pmcemot7.gif" width=3D382 =
border=3D0>=20
    </TD></TR></TBODY></TABLE><B>Which ONE of the following vectors may =
represent=20
  the acceleration due to gravity of the ball at point Q? </B><BR>
  <CENTER><IMG height=3D132 alt=3D"equations of motion diagram 7b"=20
  src=3D"http://www.sec.org.za/tests/pmcemot8.gif" width=3D551 =
border=3D2> </CENTER>
  <UL>
    <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
      <TBODY>
      <TR>
        <TD width=3D40><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ10></TD>
        <TD><B>A</B></TD></TR>
      <TR>
        <TD width=3D40><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ10></TD>
        <TD><B>B</B> </TD></TR>
      <TR>
        <TD width=3D40><B>3</B><INPUT type=3Dradio value=3D1 =
name=3DQ10></TD>
        <TD><B>C</B></TD></TR>
      <TR>
        <TD width=3D40><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ10></TD>
        <TD><B>D</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Acceleration due to gravity always pointing =
towards centre of Earth. See also questions 2, 5, and 7.")' =
type=3Dbutton value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL>
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cols=3D50></TEXTAREA></CENTER></TD></TR>
    <TR>
      <TD>
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value=3D"What are the correct answers?" =
name=3DButton></CENTER></TD></TR></TBODY></TABLE></CENTER></FORM><B>
  <DIV align=3Dright><A href=3D"http://www.sec.org.za/trmc.html">click =
here for more=20
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