\documentclass[12pt, addpoints]{exam}
%Load packages to use within the document
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{setspace}
\usepackage{layout}
\usepackage{graphics}
\usepackage{enumerate}
\usepackage{multicol}
\usepackage[shortlabels]{enumitem}
\usepackage{chemfig}
\usepackage{colortbl}
\usepackage{xcolor}
\usepackage{pgfplots}
\usepackage{geometry}
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\usepackage{tikz}
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\setlength{\parindent}{0cm} %sets the margin to 0cm
\onehalfspacing %globally change the spacing to 1.5 across the whole document
\begin{document}
\textbf{Part A -- Knowledge}\\
Multiple Choice. Write the letter of your answer in the table in Part A of the test. Please do not write on the multiple choice question sheet.
\begin{questions}
\question Which of the following is a scalar quantity?
\begin{choices}
\begin{multicols}{3}
\choice{Speed}
\choice{Velocity}
\choice{Displacement}
\choice{Acceleration}
\choice{None of the above}
\end{multicols}
\end{choices}
\question A student walks 10 m [N], then 15 m [S], and finally 5 m [N]. The students total distance and displacement are:
\begin{choices}
\begin{multicols}{3}
\choice{30 m and 0 m}
\choice{0 m and 30 m [N]}
\choice{0 m and 30 m [S]}
\choice{30 m and 5 m [N]}
\choice{0 m and 5 m [S]}
\end{multicols}
\end{choices}
\question A ball is thrown straight up into the air. While it is rising:
\begin{choices}
\choice{its velocity and acceleration are both upward.}
\choice{its velocity is upward and its acceleration is downward.}
\choice{its velocity and acceleration are both downward.}
\choice{its velocity is downward and its acceleration is upward.}
\choice{its velocity and acceleration are both decreasing.}
\end{choices}
\question An object in free fall has a constant acceleration of 9.8 m/s$^2$ directed downward. Take the downward direction to be negative. This means that:
\begin{choices}
\choice{The speed of the object increases by 9.8 m/s each second.}
\choice{The velocity of the object increases by 9.8 m/s each second.}
\choice{The velocity of the object decreases by 9.8 m/s each second.}
\choice{All of the above.}
\choice{Only (A) and (C) are correct.}
\end{choices}
\question A plane traveling north at 200 m/s turns and then travels south at 200 m/s. The change in its
velocity is:
\begin{choices}
\begin{multicols}{3}
\choice{zero}
\choice{200 m/s [N]}
\choice{200 m/s [S]}
\choice{400 m/s [N]}
\choice{400 m/s [S]}
\end{multicols}
\end{choices}
\clearpage
\question The diagram below shows a velocity--time graph for a car moving in a straight line. At point $P$ the car must be:
\begin{center}
\begin{tikzpicture}[
declare function={
func(\x)= (\x<=2) * (2*\x) +
and(\x>2, \x<=5) * (2) +
and(\x>5, \x<=7) * (5) +
(\x>7) * (\x);
}
]
\begin{axis}[
xmin=0,xmax=5,
ymin=0,ymax=5,
grid=both,
xlabel={$t$ (s)},
ylabel={$\vec{v}$ (m/s)},
width=0.5\textwidth,
height=0.3\textwidth
]
\addplot[color=red]{-0.5*(x)*(x-6)};
\node[label={90:{$P$}},circle,fill,inner sep=2pt] at (axis cs:2,4) {};
\end{axis}
\end{tikzpicture}
\end{center}
\begin{choices}
\choice{moving with zero acceleration}
\choice{moving uphill}
\choice{at rest}
\choice{speeding up}
\choice{slowing down}
\end{choices}
\question The diagram below shows a position--time graph for a car moving in a straight line. At which of the following points is the car at rest?
\begin{center}
\begin{tikzpicture}[
\begin{axis}[
xmin=-0.25,xmax=5,
ymin=-0.5,ymax=5,
grid=both,
xlabel={$t$ (s)},
ylabel={$\vec{d}$(m)},
width=0.5\textwidth,
height=0.3\textwidth
]
\addplot[smooth,color=red] coordinates {
(0,4)
(1,1)
(2,0)
(3,1)
(4,4)
(5,9)
};
\node[label={90:{$A$}},circle,fill,inner sep=2pt] at (axis cs:0,4) {};
\node[label={90:{$B$}},circle,fill,inner sep=2pt] at (axis cs:1,1) {};
\node[label={90:{$C$}},circle,fill,inner sep=2pt] at (axis cs:2,0) {};
\node[label={90:{$D$}},circle,fill,inner sep=2pt] at (axis cs:3,1) {};
\node[label={90:{$E$}},circle,fill,inner sep=2pt] at (axis cs:4,4) {};
\end{axis}
\end{tikzpicture}
\end{center}
\begin{choices}
\choice{point A}
\choice{point B}
\choice{point C}
\choice{point D}
\choice{point E}
\end{choices}
\clearpage
\question A ball is thrown straight up into the air. It is caught at the same position from where it was thrown. Take the upward direction to be positive. Which of the following velocity--time graphs correctly depict this motion?
\begin{choices}
\begin{multicols}{2}
\choice{\hspace{0.20in} \\
\begin{tikzpicture}[
\begin{axis}[ticks=none,
axis lines = middle,
xmin=0,xmax=5,
ymin=-5,ymax=5,
xlabel={$t$},
ylabel={$\vec{v}$},
width=0.3\textwidth,
height=0.25\textwidth
]
\addplot[color=red]{-1.5*x+3.5};
\end{axis}
\end{tikzpicture}
}
\choice{\hspace{0.20in} \\
\begin{tikzpicture}[
\begin{axis}[ticks=none,
axis lines = middle,
xmin=0,xmax=5,
ymin=-5,ymax=5,
xlabel={$t$},
ylabel={$\vec{v}$},
width=0.3\textwidth,
height=0.25\textwidth
]
\addplot[smooth,color=red] coordinates {
(0,2.5)
(0.5,2)
(1,1.5)
(1.5,1)
(2,0.5)
(2.25,0.25)
(2.4,0.1)
(2.5,0)
(2.6,0.1)
(2.75,0.25)
(3,0.5)
(3.5,1)
(4,1.5)
(4.5,2.0)
(5,2.5)
};
\end{axis}
\end{tikzpicture}
}
\choice{\hspace{0.20in} \\
\begin{tikzpicture}[]
\begin{axis}[ticks=none,
axis lines = middle,
xmin=0,xmax=4.5,
ymin=-5,ymax=5,
xlabel={$t$},
ylabel={$\vec{v}$},
width=0.3\textwidth,
height=0.25\textwidth
]
\addplot[color=red]{-0.75*x*(x-4.5)};
\end{axis}
\end{tikzpicture}
}
\choice{\hspace{0.20in} \\
\begin{tikzpicture}[]
\begin{axis}[ticks=none,
axis lines = middle,
xmin=0,xmax=5,
ymin=-5,ymax=5,
xlabel={$t$},
ylabel={$\vec{v}$},
width=0.3\textwidth,
height=0.25\textwidth
]
\addplot[color=red]{1.5*x-3.5};
\end{axis}
\end{tikzpicture}
}
\end{multicols}
\end{choices}
\question The area under a velocity--time graph represents:
\begin{choices}
\begin{multicols}{3}
\choice{acceleration}
\choice{total distance}
\choice{speed}
\choice{change in displacement}
\choice{displacement}
\end{multicols}
\end{choices}
\question The area under an acceleration--time graph represents:
\begin{choices}
\begin{multicols}{3}
\choice{acceleration}
\choice{total distance}
\choice{speed}
\choice{change in velocity}
\choice{displacement}
\end{multicols}
\end{choices}
\question A stone is released from rest from the edge of a building roof that is 190 m above the ground. Neglecting air resistance, the speed of the stone, just before striking the ground, is:
\begin{choices}
\begin{multicols}{3}
\choice{43 m/s}
\choice{61 m/s}
\choice{120 m/s}
\choice{190 m/s}
\choice{1,400 m/s}
\end{multicols}
\end{choices}
\question A ball rolls up a slope. At 3.0 seconds its velocity is 20.0 m/s [E]; at 8.0
seconds its velocity is 0.0 m/s. What is the average acceleration from 3.0 to 8.0 s?
\begin{choices}
\begin{multicols}{3}
\choice{2.5 m/s$^2$ [E]}
\choice{4.0 m/s$^2$ [W]}
\choice{5.0 m/s$^2$ [W]}
\choice{6.0 m/s$^2$ [W]}
\choice{9.8 m/s$^2$ [E]}
\end{multicols}
\end{choices}
\clearpage
\question Of the following situations, which one is impossible?
\begin{choices}
\choice{A body having velocity east and acceleration east}
\choice{A body having velocity east and acceleration west}
\choice{A body having zero velocity and non-zero acceleration}
\choice{A body having constant acceleration and variable velocity}
\choice{A body having constant velocity and variable acceleration}
\end{choices}
\question A racing car traveling with constant acceleration increases its speed from 10 m/s to 50 m/s over a distance of 60 m. How long does this take?
\begin{choices}
\begin{multicols}{2}
\choice{2.0 s}
\choice{4.0 s}
\choice{5.0 s}
\choice{8.0 s}
\choice{The time cannot be calculated since the speed is not constant}
\end{multicols}
\end{choices}
\question An object is thrown vertically upward with a certain initial velocity in a world where the
acceleration due to gravity is 19.6 m/s$^2$. Neglecting air resistance, if this object reaches a height of $h$ on the Earth, then on this new planet, its height in terms of $h$ is:
\begin{choices}
\begin{multicols}{2}
\choice{$h/2$}
\choice{$\sqrt{2} h$}
\choice{$2h$}
\choice{$4h$}
\choice{it will reach the same height}
\end{multicols}
\end{choices}
\end{questions}
\clearpage
\begin{center}
SPH3UE: Pre--AP Physics, Grade 11, University Preparation \\
Test \#1: Preliminary Skills
\end{center}
Name: \rule{2.5in}{0.4pt} \hfill Date: \rule{2.5in}{0.4pt}\\
\begin{table}[h]
\label{sample_table1.1}
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
\hspace{0.15in} {Knowledge} \hspace{0.15in} & \hspace{0.15in} {Thinking} \hspace{0.15in} & \hspace{0.15in} {Communication} \hspace{0.15in} & \hspace{0.15in} {Application} \hspace{0.15in}\\
\hline
& & & \\
\hfill {/15} & \hfill {/15} & \hfill {/17} & \hfill {/18} \\
& & & \\
\hline
\end{tabular}
\end{center}
\end{table}
\vspace{-0.25in}
Communication will be evaluated on certain specific communication--style questions as well as throughout the test. Communication skills will be evaluated on significant digits, proper use of units, properly labeled diagrams, and a well--organized solution. \\
Instructions:
\begin{itemize}
\item{Please do not begin the test until instructed to do so.}
\item{Please clear your desk of all belongings other than a pen/pencil, eraser, and non-graphing calculator.}
\item{Fully answer all questions using complete sentences (where appropriate) and proper mathematical form.}
\item{Budget your time on each question accordingly. Do not spend too much time on any one question and be sure to answer the questions you know how to do first.}
\item{A formula sheet is provided.}
\item{A multiple choice question sheet is provided. Please do not write on the multiple choice question sheet. Transfer your answers to the table in Part A of the test.}
\item{Try not to leave any questions blank. Write down anything that comes to mind.}
\item{Good luck!}
\end{itemize}
\clearpage
\textbf{Part A: Knowledge} (15 marks)\\
\vspace{-0.10in}
Multiple choice. Write the letter of your answer in the table below.
\begin{table}[h]
\label{sample_table1.1}
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
1. \hspace{0.25in} & 2. \hspace{0.25in} & 3. \hspace{0.25in} & 4. \hspace{0.25in} & 5. \hspace{0.25in} & 6. \hspace{0.25in} & 7. \hspace{0.25in} & 8. \hspace{0.25in} \\
\hline
& & & & & & & \\
& & & & & & & \\
\hline
9. \hspace{0.25in} & 10. \hspace{0.25in} & 11. \hspace{0.25in} & 12. \hspace{0.25in} & 13. \hspace{0.25in} & 14. \hspace{0.25in} & 15. \hspace{0.25in} & 16. \hspace{0.25in} \\
\hline
& & & & & & & \cellcolor{black!100} \\
& & & & & & & \cellcolor{black!100} \\
\hline
\end{tabular}
\end{center}
\end{table}
\vspace{-0.10in}
\textbf{Part B: Thinking} (15 marks)
\begin{enumerate}
\item{Mr. Clements is running toward an avocado tree at a constant speed of 11 m/s. At the instant when Mr. Clements is 19 m away from the tree, an avocado begins to fall. If the hanging avocado was 15 m above the ground just before it fell, determine if the avocado will hit Mr. Clements. Draw a diagram describing this problem. [5T, 2C]}
\newpage
\item{After several races with Alice, Bob is bored and decided to try out skydiving.
\begin{enumerate}[(a)]
\item{Starting from rest, Bob jumps out of an airplane. After 6.5 s, Bob reaches a speed of 56 m/s directed toward the Earth. Determine Bob's acceleration during this time interval. [2T]}
\vfill
\item{Is the air resistance acting on Bob negligible? Justify your reasoning. [2C]}
\vfill
\item{From 6.5 to 10.0 s, Bob is falling at a constant speed of 56 m/s. At 10.0 s, Bob deploys his parachute. From the moment Bob deploys his parachute, he falls 456 m and reaches a final velocity of 5.6 m/s [down]. Determine Bob's acceleration during this interval. [2T]}
\vfill
\item{From this moment onward, Bob is moving at terminal velocity. Exactly 3 minutes and 15 seconds later, Bob lands safely on the ground. From what height above the ground did Bob jump out of the airplane? [4T, 1C]}
\vfill
\vspace{0.75in}
\item{What was Bob's average acceleration during the entire trip? [2T]}
\vfill
\end{enumerate}
}
\end{enumerate}
\newpage
\textbf{Part D -- Communication} (12 marks)
\begin{enumerate}[resume]
\item{A basketball is dropped and accelerates toward the ground. It hits the ground, bounces and travels upward to the same position from where it was dropped. Assume that the basketball is in contact with the ground for an instant. Sketch a position--time, velocity--time, and acceleration--time graph for the motion of the ball. Take up to be the positive direction. [6C]
\begin{multicols}{3}
\begin{tikzpicture}[
\begin{axis}[ticks=none,
axis lines = middle,
xmin=0,xmax=5,
ymin=-5,ymax=5,
xlabel={$t$},
ylabel={$\vec{d}$},
width=0.38\textwidth,
height=0.35\textwidth
]
%\addplot[color=red]{-1.5*x+3.5};
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}[
\begin{axis}[ticks=none,
axis lines = middle,
xmin=0,xmax=5,
ymin=-5,ymax=5,
xlabel={$t$},
ylabel={$\vec{v}$},
width=0.38\textwidth,
height=0.35\textwidth
]
%\addplot[color=red]{-1.5*x+3.5};
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}[
\begin{axis}[ticks=none,
axis lines = middle,
xmin=0,xmax=5,
ymin=-5,ymax=5,
xlabel={$t$},
ylabel={$\vec{a}$},
width=0.38\textwidth,
height=0.35\textwidth
]
%\addplot[color=red]{-1.5*x+3.5};
\end{axis}
\end{tikzpicture}
\end{multicols}
}
\item{Describe a specific situation where an object has:
\begin{enumerate}[(a)]
\item{a non--zero average speed and average velocity of 0 m/s. [2C]}
\vfill
\item{increasing speed and decreasing velocity. [2C]}
\vfill
\item{zero velocity and non--zero acceleration. [2C]}
\vfill
\end{enumerate}
}
\end{enumerate}
\newpage
\end{enumerate}
\end{document}
