Applied Mathematics Regents Exam Questions (Physics) – Regression
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Conversion Practice
1) When one gram of gasoline burns in a car's engine, the amount of energy given off is approximately
1.03 x 104 cal. Express this quantity in joules (J). (Use 1 cal = 4.184 J).
2) The pressure reading from a barometer is 742 mm Hg. Express this reading in kilopascals, kPa. (Use 760
mm Hg = 1.013 x 105 Pa).
3) How many mega years is equivalent to 6.02 × 1023 nanoseconds (ns) if you ignore leap years?
4) The average student is in class 330 min/day.
a. How many hours/day is the average student in class? You should know what conversion factors
you will need!
b. How many seconds is the average student in class per week?
c. Calculate how many seconds you are in class a day (pick any weekday you have class). Show any
calculations you have to do as dimensional analysis. Answers will vary between you and your
classmates.
5) Approximately how many pounds do you weigh? ___________ lbs.
The human body is approximately 60% water by mass. You can write this as a conversion factor: 60 lb
water / 100 lb body mass. (Does this make sense?) Using that conversion factor, how many pounds of
water are there in your body? (This is a rough estimate, since it also depends on body fat).
6) French cooks usually weigh ingredients. A French recipe uses 225 grams of granulated sugar. How many
cups are needed if there are 2 cups of sugar per pound of sugar? Round to the nearest cup.
(Note that you are changing from units of weight, grams, to units of volume, cups. The conversion factor
2 cups per pound is true for sugar but may not be the same for all other ingredients.) (1 lb = 453.6g)
7) A car accelerates at 12 mi/hr·s (miles per hour-seconds). Write that acceleration in m/s2. (1 mile = 1.609
km)
8) Because your 18 year-old friend never learned dimensional analysis, he started working at a fast food
restaurant wrapping hamburgers. Every 3 hours he wraps 350 hamburgers. He works 8 hours per day.
He works 5 days a week. He gets paid every 2 weeks with a salary of $440.34 (after taxes!).
a. Approximately how many hamburgers will he have to wrap to make his first one million dollars?
(If you can solve the problem, you know dimensional analysis and maybe you can teach your
friend so that he can get a better job!) This will be an estimate, so round to 1 significant figure.
Explicitly show all conversions in your setup.
b. How much time will it take to wrap all those hamburgers (given as your answer to part a)?
Express the time in years. Assume that he will work 40 weeks out of the year and that he works
with the same efficiency everyday. By the way, be careful on this one—no one works 24 hours a
day! Round your answer to the nearest year.
c. How old will he be when he makes his first million? (Let’s hope he makes it to this ripe old age!)
Applied Mathematics Regents Exam Questions (Physics) – Regression
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1
The data were obtained by varying the force applied to a spring and measuring the
corresponding elongation of the spring.
a) Using the information in the table, construct a graph on the grid following the
directions below. Mark an appropriate scale on the axis labeled "Elongation (m)." Plot
the data points for force versus elongation.
b) Draw the best-fit line.
c) Using the best-fit line, determine the spring constant of the spring. [Show all
calculations, including the equation and substitution with units.]
Applied Mathematics Regents Exam Questions (Physics) – Regression
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2
A car is traveling due north at 24.0 meters per second when the driver sees an obstruction
on the highway. The data table below shows the velocity of the car at 1.0-second
intervals as it is brought to rest on the straight, level highway.
a) Using the information in the data table, construct a graph on the grid, following the
directions below. Plot the data points for velocity versus time.
b) Draw the best-fit line.
Applied Mathematics Regents Exam Questions (Physics) – Regression
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A photoemissive metal was illuminated successively by photons of various
frequencies. The maximum kinetic energies of the emitted photoelectrons were
measured and recorded in the table below.
a) Using the information in the data table, construct a graph on the grid provided on
your answer paper, following the directions below. Plot the data points for maximum
kinetic energy versus frequency.
b) Draw the best-fit line.
c) Determine the slope of the graph. [Show all calculations, including the equation
and substitution with units.]
Applied Mathematics Regents Exam Questions (Physics) – Regression
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A variable resistor was connected to a battery. As the resistance was adjusted, the
current and power in the circuit were determined. The data are recorded in the table
below.
Using the information in the data table, construct a line graph on the grid provided,
following the directions below.
a) Plot the data points for power versus current.
b) Draw the best-fit line.
c) Using your graph, determine the power delivered to the circuit at a current of 3.5
amperes.
d) Calculate the slope of the graph. [Show all calculations, including the equation
and substitution with units.]
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In a laboratory exercise, a student kept the mass and amplitude of swing of a simple
pendulum constant. The length of the pendulum was increased and the period of the
pendulum was measured. The student recorded the data in the table below.
a) Using the information in the table, construct a graph on the grid. Label each axis
with the appropriate physical quantity and unit. Mark an appropriate scale on each
axis. Plot the data points for period versus pendulum length.
b) Draw the best-fit line or curve for the data graphed.
c) Using your graph, determine the period of a pendulum whose length is 0.25 meter.
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In an experiment, a student measured the length and period of a simple pendulum.
The data table lists the length (ℓ) of the pendulum in meters and the square of the
period (T2) of the pendulum in seconds2.
a) Using the information in the data table, construct a graph on the grid. Plot the
data points for the square of period versus length. Draw the best-fit straight line.
b) Using your graph, determine the time in seconds it would take this pendulum to
make one complete swing if it were 0.200 meter long.
4 2
)
g
where g represents the acceleration due to gravity. Explain how the graph you have
drawn could be used to calculate the value of g. [You do not need to perform any
actual calculations.]
c) The period of a pendulum is related to its length by the formula: T 2  (
Applied Mathematics Regents Exam Questions (Physics) – Regression
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In an experiment, a student applied various forces to a spring and measured the
spring’s corresponding elongation. The table below shows his data.
a) On the grid, plot the data points for force versus elongation. Draw the best-fit
line.
b) Using your graph, calculate the spring constant of the spring. [Show all work,
including the equation and substitution with units.]
Applied Mathematics Regents Exam Questions (Physics) – Regression
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An experiment was performed using various lengths of a conductor of uniform crosssectional area. The resistance of each length was measured and the data recorded in
the table below.
a) Using the information in the data table, construct a graph on the grid. Mark an
appropriate scale on the axis labeled “Length (m).” Plot the data points for resistance
versus length. Draw the best-fit line.
b) Calculate the slope of the best-fit line. [Show all work, including the equation and
substitution with units.]
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Answers
Unit Conversions
1) 43095 J or 4.31 x 104 J
2) 98.9 kPa
3) 19.1 My
4) A. 5.5 h/day
B. 9.9 x 104 s
C. Answers will vary
5) 150lbs: 90 lbs water
6) About 1 cup
7) 5.4 m/s2
8) A. 2 x 107 burgers
B. 114 years
C. 132 years
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Answers – Graphing
1
a)
b) The best-fit line must be straight.
c)
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a)
b) The best-fit line must be straight.
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a)
b) The best-fit line must be straight.
c)
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a)
b) Allow 1 credit for drawing a straight best-fit line.
c) 10.5 W ± 0.3 W
d)
Applied Mathematics Regents Exam Questions (Physics) – Regression
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a)
b) 0.89 (± .1) seconds, or an answer consistent with the student’s graph.
c)
Applied Mathematics Regents Exam Questions (Physics) – Regression
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a)
b)
Applied Mathematics Regents Exam Questions (Physics) – Regression
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a)
b)
Answer to Formula Manipulation