hoskerelab/PE_Civil_Bench huggingface dataset:
Subdiscipline: math

\textbf{Question 1:} If the equation of a curve is known, which of the following can be determined using integration? \\

\textbf{A.} The slope or concavity of the curve \\
\textbf{B.} The location of the inflection points on the curve \\
\textbf{C.} The number of inflection points on the curve \\
\textbf{D.} Area under the curve bounded by two limits \\

Answer: D
Subdiscipline: math

\textbf{Question 2:} For any function \( y = f(x) \), the derivative is defined as:  \\
\(\frac{dy}{dx}\) 

Which of the following represents the correct definition of the derivative?

\bigskip

\textbf{A.}  
\(\frac{dy}{dx} = \lim_{\Delta x tend to 0} \frac{\Delta y}{\Delta x}\)

\textbf{B.}  
\(\frac{dy}{dx} = \lim_{\Delta y tend to 0} \frac{\Delta y}{\Delta x}\)

\textbf{C.}  
\(\frac{dy}{dx} = \lim_{\Delta x tend to 0} \frac{f(x+\Delta x) - f(x)}{\Delta x}\)

\textbf{D.} Both A and C \\

Answer: D
Subdiscipline: math

\textbf{Question 3:} A line passes through \( (4, 5) \) and is parallel to the line \( 2y = 3x + 6 \). The equation of the line is most nearly: 

\bigskip

\textbf{A.} \( y = \frac{2}{3}x \) \\

\textbf{B.} \( 3x - 2y - 2 = 0 \) \\

\textbf{C.} \( y = \frac{2}{3}x - 1 \) \\

\textbf{D.} \( 2x - 3y - 1 = 0 \)  \\

Answer: B
Subdiscipline: math

\textbf{Question 4:} The shortest distance between two points, \( (-4, -5) \) and \( (7, 13) \), is most nearly:

\bigskip

\text{A. } 19 \text{ units}

\text{B. } 21 \text{ units}

\text{C. } 23 \text{ units}

\text{D. } 25 \text{ units} \\

Answer: B
Subdiscipline: math

\textbf{Question 5:} What are the roots of the equation, \( 5 (x^4 - 4x^3 + 3x^2) = 0 \)?  

\bigskip

\text{A. } 0, 2, 3

\text{B. } 0, 1, 3

\text{C. } 0, 1, 4

\text{D. } 0, \pm 2

Answer: B
Subdiscipline: math

\textbf{Question 6:} Which of the following is the general solution to the differential equation?  
\( \frac{dy}{dt} + 3y = 0 \quad \text{if} \quad y(0) = 2 \)

\bigskip

\text{A. } y = 3e^{-2t}

\text{B. } y = 3 \sin(t) + 2 \cos(t)

\text{C. } y = 3e^{-2t} + 2e^{-3t}

\text{D. } y = 2e^{-3t}

Answer: D
Subdiscipline: math

\textbf{Question 7:} The equation of a circle is given as \( x^2 + y^2 + 3x + 4y = 0 \). The coordinates of the center are most nearly:

\bigskip

\begin{array}{ll} \text{A.} & (1.5, 2) \\ \text{B.} & (-1.5, 2) \\ \text{C.} & (-1.5, -2) \\ \text{D.} & (1.5, -2) \end{array}

Answer: C
Subdiscipline: water resources

\textbf{Question 8:} A conduit is carrying less than half-full of water as shown below. The water in the conduit subtends an angle of 135 degrees at the center. The radius of the conduit is 2 ft. The area of the water is most nearly:

\bigskip

\text{A. } 2.3 \text{ ft}^2

\text{B. } 3.3 \text{ ft}^2

\text{C. } 4.3 \text{ ft}^2

\text{D. } 4.3 \text{ ft}^2

Answer: B
Subdiscipline: math

\textbf{Question 9:} What is the value of \( x \) if \( \log_5(x + 6) + \log_5(x + 2) = 1 \)?

\bigskip

\text{A. } \partial - l

\text{B. } \partial - 7

\begin{array}{ll} \text{C.} & 1 \\ \text{D.} & 7 \end{array}

Answer: A
Subdiscipline: structural

\textbf{Question 10:} A force of 10 kN is acting along AB, where \( A = (1, 1, 3) \) and \( B = (7, 3, 4) \). The vector representation of the force is most nearly:

\bigskip

\text{A. } F = 9.375i + 3.125j + 1.5625k

\text{B. } F = 2.375i + 0.125j + 5.5625k

\text{C. } F = 9.375i + 1.125j + 1.5625k

\text{D. } F = 9.375i + 3.125j + 7.5625k

Answer: A
Subdiscipline: math

\textbf{Question 11:} What is the inverse of the following matrix?  
\[ \begin{bmatrix} 5 & -3 \\ 3 & -2 \end{bmatrix} \]

\bigskip

\text{A. } \left[\begin{array}{cc} -2 & 3 \\ 3 & -5 \end{array}\right]

\text{B. } \left[\begin{array}{cc} 2 & -3 \\ 3 & -5 \end{array}\right]

\text{C. } \left[\begin{array}{cc} 5 & \partial \\ -3 & 2 \end{array}\right]

\text{D. } \left[\begin{array}{cc} 2 & -3 \\ -3 & 5 \end{array}\right]

Answer: B
Subdiscipline: math

\textbf{Question 12:} The value of \[ \int_{1}^{2}\left(\frac{(x^{2}-1)^{2}}{x^{2}}\right)dx \] is most nearly:

\bigskip

\text{A. } \frac{-2}{5}

\text{B. } \frac{1}{2}

\text{C. } -1

\text{D. } \frac{5}{6}

Answer: D
Subdiscipline: math

\textbf{Question 13:} The standard deviation of the data: 13, 7, 12, 10, 18 is most nearly:

\bigskip

\text{A. } 2.97

\text{B. } 4.33

\text{C. } 5.22

\text{D. } 3.63

Answer: D
Subdiscipline: math

\textbf{Question 14:} What is the population variance of the following data set: 13, 17, 12, 10, 18?

\bigskip

\text{A. } 7.2

\text{B. } 4.9

\text{C. } 12.5

\text{D. } 9.2

Answer: D
Subdiscipline: math

\textbf{Question 15:} What is the sample variance of the following data set? 13, 17, 12, 10, 18

\bigskip

\text{A. } 9.2

\text{B. } 10.2

\text{C. } 11.5

\text{D. } 12.2

Answer: C
Subdiscipline: math

\textbf{Question 16:} In a class, 7 students scored 80\%, 3 students scored 90\%, and 11 students scored 60\%. The average/mean score in that class is most nearly:

\bigskip

\text{A. } 66\%

\text{B. } 71\%

\text{C. } 76\%

\text{D. } 78\%

Answer: B
Subdiscipline: math

\textbf{Question 17:} The table below shows the distribution of exam scores. The approximate mean and mode of this distribution are most nearly:

\bigskip

\begin{array}{|c|c|} \hline \textbf{Score} & \textbf{Frequency} \\ \hline 45 & 2 \\ 63 & 3 \\ 68 & 2 \\ 70 & 4 \\ 71 & 2 \\ 85 & 5 \\ 87 & 3 \\ 90 & 1 \\ \hline \end{array}

\bigskip

\text{A. } 73.3, 70

\text{B. } 73.3, 71

\text{C. } 73.3, 85

\text{D. } 27.6, 70

Answer: C
Subdiscipline: water resources

\textbf{Question 18:} A new 200 mm diameter pipeline is installed over a distance of 1000 m. Annual maintenance and pumping costs are considered to be paid in their entirety at the end of the years in which their costs are incurred. The pipe has the following costs and properties:

\begin{itemize} \item Initial cost: \$1350 \item Annual interest rate: 6\% \item Service life: 6 years \item Salvage value: \$120 \item Annual maintenance: \$500 \item Pump cost/hour: \$2.75 \item Pump operation: 2000 hours/year \end{itemize}

\bigskip

\text{Options:}

\begin{itemize} \item (A) \$5700 \item (B) \$5900 \item (C) \$6100 \item (D) \$6300 \end{itemize}

Answer: D
Subdiscipline: construction

\textbf{Question 19:} Materials are best managed with the concept of:

\bigskip

\text{A.} Buying everything in advance to make sure it is available when needed

\text{B.} Buying and delivering at installation time so we don't need to store anything

\text{C.} Minimize overall cost by taking a balanced approach between A and B

\text{D.} None of the above

Answer: C
Subdiscipline: math

\textbf{Question 20:} The following schedule of funds is available to form a sinking fund. 
\[ \begin{array}{ll} t = 0 \text{ yr:} & \$5000 \\ t = 1 \text{ yr:} & \$4000 \\ t = 2 \text{ yr:} & \$3000 \\ t = 3 \text{ yr:} & \$2000 \end{array} \]

At the end of the fourth year, equipment costing \$25,000 will have to be purchased as a replacement for old equipment. Money is valued at 20\% by the company. At the time of purchase, how much money will be needed?

\textbf{A.} \$820

\textbf{B.} \$1000

\textbf{C.} \$2000

\textbf{D.} \$8200

Answer: B
Subdiscipline: construction

\textbf{Question 21:} In earned value analysis (EVA), we found: BCWP = \$32,600, BCWS = \$29,650, and ACWP = \$33,900.

\textbf{A.} Behind schedule and over budget

\textbf{B.} Behind schedule and under budget

\textbf{C.} Ahead of schedule and over budget

\textbf{D.} Ahead of schedule and under budget

Answer: C
Subdiscipline: construction

\textbf{Question 22:} An updated schedule is:

\textbf{A.} A schedule that reflects new design modifications

\textbf{B.} A revised schedule reflecting project information at a given date regarding completed activities, in-progress activities, and changes in future work

\textbf{C.} A schedule that incorporates subcontractors' schedules

\textbf{D.} A schedule with resources and budget

Answer: B
Subdiscipline: ethics

\textbf{Question 23:} You are invited to have a job-site interview in Kansas City by ABC Company. They already paid for your airfare and hotel and advised you to submit the other expenses such as meals, taxis, and car parking after the interview. While you are preparing to fly, another company, XYZ, also called you to have an interview just after the following date at the same city. Assume no conflict arises between these two interview schedules, including the flight times, etc. What should you do?

\textbf{A.} Accept the interview at XYZ Company without informing ABC Company as there is no time conflict

\textbf{B.} Accept the interview at XYZ Company informing ABC Company but ask for reimbursement about 50\% from each company

\textbf{C.} Accept the interview at XYZ Company informing ABC Company but ask for reimbursement from ABC Company only as they already paid

\textbf{D.} Reject the interview at XYZ Company due to conflict of interest

Answer: B
Subdiscipline: ethics

\textbf{Question 24:} A professional engineer licensed about 35 years is offered a job in a newly established company with a well-developed computerized control system for traffic engineering. That computerized control system was not available 35 years back when he obtained the original license. The engineer may accept this job offer if:

\textbf{A.} He took a class on that computerized control system sometime during his career

\textbf{B.} His license was always in good standing status

\textbf{C.} His original specialization was traffic engineering

\textbf{D.} He is competent in the area of computerized control system

Answer: D
Subdiscipline: construction

\textbf{Question 25:} The concept of resource leveling works by:

\textbf{A.} Reducing the amounts of resources allocated to some activities

\textbf{B.} Starting activities on their late start dates

\textbf{C.} Shifting non-critical activities within their available float

\textbf{D.} Limiting the amount of resources any activity can obtain

Answer: C
Subdiscipline: construction

\textbf{Question 26:} If a construction project accelerates compared to its original schedule, the indirect cost:

\textbf{A.} Increases at an increasing rate

\textbf{B.} Increases at a decreasing rate

\textbf{C.} Increases at a steady rate

\textbf{D.} Decreases at a steady rate

Answer: D
Subdiscipline: ethics

\textbf{Question 27:} While sending an electronic report to someone, the sender has to make sure (check all that apply):

\textbf{A.} The recipient's e-mail system accepts attachments

\textbf{B.} The recipient can open that file type

\textbf{C.} The recipient is in the same timezone

\textbf{D.} The attached file is no more than 2 MB in size

Answer: A, B
Subdiscipline: construction

\textbf{Question 28:} While excavating, the contractor hits a rock layer. Since the plans and soil report did not mention such rock, the contractor files a claim under:

\textbf{A.} Force majeure

\textbf{B.} Differing site conditions

\textbf{C.} Design errors/omissions

\textbf{D.} Unusual weather conditions

\textbf{E.} Changes in owner's requirements

Answer: B
Subdiscipline: construction

\textbf{Question 29:} After performing forward and backward passes, you found that for a certain activity, the Early Start date is later than the Late Start date. Your explanation is mostly:

\textbf{A.} This is impossible. You must have done a mathematical error.

\textbf{B.} This activity is not critical; it has some leeway (float).

\textbf{C.} This activity was placed in the wrong position in the network.

\textbf{D.} You have used an "imposed finish date" for the project or the activity that is earlier than the Late Start date.

Answer: D
Subdiscipline: construction

\textbf{Question 30:} The forward pass is:

\textbf{A.} A subnet of the CPM network that includes all activities to be done first

\textbf{B.} A process called "start to finish" calculating early dates for each activity

\textbf{C.} Assigning logic relationships for succeeding activities

\textbf{D.} A and C'

Answer: B
Subdiscipline: math

\textbf{Question 31:} A company can manufacture a product using hand tools with a tool cost of \$1,750, and the cost per unit is \$1.75. As an alternative, an automated system will cost \$230,000 with a manufacturing cost per unit of \$0.25. With an anticipated annual volume of 75,000 units and neglecting interest, the break-even point or the payback time in years is most nearly:

\textbf{A.} 2 years

\textbf{B.} 3 years

\textbf{C.} 4 years

\textbf{D.} 5 years

Answer: A
Subdiscipline: construction

\textbf{Question 32:} Activity A has 6 days of total float and 2 days of free float. If activity A is delayed 4 days, which statement is correct:

\textbf{A.} The project will finish 2 days late

\textbf{B.} Nothing will be impacted

\textbf{C.} The successors of Activity A will also be delayed by 4 days

\textbf{D.} The completion date of the project will not be impacted but the successors will be impacted

Answer: D
Subdiscipline: construction

\textbf{Question 33:} A construction company purchased a front loader with an initial cost of \$14,000. The annual interest rate is 2\%. The annual maintenance cost is \$350 and is considered to be paid at the end of each year. Using the MACRS depreciation system, what is most nearly the depreciation for the front loader in the first three years of operation assuming a ten years recovery period?

\textbf{A.} \$2,600

\textbf{B.} \$5,940

\textbf{C.} \$4,940

\textbf{D.} \$5,490

Answer: B
Subdiscipline: structural

\textbf{Question 34:} A simply supported reinforced concrete beam 12 in wide and 28 in deep spans 20 ft. The beam is subjected to a uniform service dead load equal to 2.0 kips/ft (exclusive of beam weight) and to a uniform service live load of 2.4 kips/ft. The factored uniform load is most nearly:

\textbf{Options:}

\begin{itemize} \item (A) 6.7 kips/ft \item (B) 7.4 kips/ft \item (C) 8.0 kips/ft \item (D) 9.2 kips/ft \end{itemize}

Answer: A
Subdiscipline: structural

\textbf{Question 35:} Three forces are acting on a point (at origin). 100 N along positive x-axis, 800 N at an angle of 120 degree clockwise with x-axis along positive z-axis and 260 N at an angle of 22.62 degree counter clockwise with y-axis in second quadrant of xy plane. What is the magnitude of the resultant force?

\textbf{A.} 604 N

\textbf{B.} 545 N

\textbf{C.} 435 N

\textbf{D.} 673 N

Answer: A
Subdiscipline: structural

\textbf{Question 36:} A solid cylinder weighing 300 N rests between two frictionless walls. The vertical wall makes 68.2 degree angle with the bottom surface. The ball touches at point B with vertical wall and point A on the surface. What is the wall reaction at B in Newton?

\textbf{A.} 328

\textbf{B.} 120

\textbf{C.} 898

\textbf{D.} 0

Answer: B
Subdiscipline: structural

\textbf{Question 37:} A 10 ft long, 14 inch wide, and 22 inch deep reinforced concrete beam has reinforcement placed at 18 inches from the top of the beam. The beam is subjected to a uniformly distributed dead load of 12 pound-force/feet and a point load of 50,000 pound-force at the middle of the beam. The beam is underreinforced. The concrete and reinforcing steel properties are:

\[ f'_c = 2500 \, \text{lbf/in}^2, \quad f_y = 50,000 \, \text{lbf/in}^2, \quad A_s = 3.8 \, \text{in}^2 \]

The beam supports a concentrated live load of 50,000 lbf. Neglecting the self-weight of the beam, the minimum amount of shear reinforcement required for a center-to-center stirrup spacing of 12 inches under ACI strength design specifications is most nearly:

\textbf{Options:}

\begin{itemize} \item (A) 0.1 in² \item (B) 0.2 in² \item (C) 0.3 in² \item (D) 0.4 in² \end{itemize}

Answer: D
Subdiscipline: structural

\textbf{Question 38:} A 2-m cubic block is in equilibrium condition on an inclined plane as shown below. If the inclination is raised, the block will intend to overturn when \( \theta \) equals:

\textbf{A.} 30°

\textbf{B.} 37.5°

\textbf{C.} 45°

\textbf{D.} 55°

Answer: C
Subdiscipline: structural

\textbf{Question 39:} A small pulley with static friction coefficient \( \mu_s = 0.3 \) and kinetic friction coefficient \( \mu_k = 0.2 \) is attached to a ceiling. A wire runs across this pulley where, at one end, a 100 kg object is attached and subjected to gravity. The wire from the other end runs down and moves along another bigger pulley with \( \mu_s = 0.3 \) and \( \mu_k = 0.2 \). The same wire runs along this pulley, and a tension \( T \) is applied upwards at the end.

For the following friction pulley system, how much load is required to be applied at the end of the pulley to make the 100 kg object begin to rise?

\textbf{A.} 150 N

\textbf{B.} 981 N

\textbf{C.} 3,260 N

\textbf{D.} 6,460 N

Answer: D
Subdiscipline: structural

\textbf{Question 40:} A 90-kg man is hanging using two cables. The cable AB is attached to the ceiling and is making an angle of 20 degree with the ceiling. Another cable BC is attached to the vertical wall. Point A (ceiling) is left of the point C(vertical wall) and point A is higher than point C. Both cables meet at B where the person is hanging. The tension in cable AB is most nearly:

\textbf{A.} 2,581 kN

\textbf{B.} 2.58 kN

\textbf{C.} 2.581 kg

\textbf{D.} 2.58 N

Answer: B
Subdiscipline: structural

\textbf{Question 41:} A cable is stretched between points A and B, where point B is 18 feet lower in elevation than point A. At point C, located 45 feet to the right of point A, a 400 lb object is hanging, causing point C to be 15 feet lower than point A. Additionally, an unknown weight is suspended at point D, which is 30 feet to the right of point C. Point D is 20 feet below point A. If point B is positioned 125 feet to the right of point A, what is the tension in the cable segment between points C and D? Assume the cable is weightless and the system is in equilibrium.

\textbf{A.} 1,880 lb

\textbf{B.} 480 lb

\textbf{C.} 320 lb

\textbf{D.} 2,432 lb

Answer: D
Subdiscipline: structural

\textbf{Question 42:} A rectangular section has 44 inch depth and 24 inch width. The rectangle has a rectangular hole of size 10 inch wide and 20 inch deep at the middle. The moment of inertia of the following section about the centroidal vertical-axis is most nearly:

\textbf{A.} 94,021 in\(^4\)

\textbf{B.} 49,021 in\(^4\)

\textbf{C.} 4,200 in\(^4\)

\textbf{D.} 4,700 in\(^4\)

Answer: B
Subdiscipline: structural

\textbf{Question 43:} A W-shape member (yield strength of 36 ksi; ultimate strength of 58 ksi) carries an axial live tensile load of 420 kips. The member's flanges are bolted to a connection bracket. The shear lag factor for the connection is 0.90. The required net area based on the fracture (rupture) criterion is most nearly:

\textbf{Options:}

\begin{itemize} \item (A) 12 in\(^2\) \item (B) 17 in\(^2\) \item (C) 22 in\(^2\) \item (D) 27 in\(^2\) \end{itemize}

Answer: B
Subdiscipline: structural

\textbf{Question 44:} A square element is subjected to a compressive stress of 5 psi on its top and bottom faces, and a compressive stress of 10 psi on both side faces. Given this plane stress condition, the maximum in-plane shear stress is most nearly:

\textbf{A.} 2.5 psi

\textbf{B.} 5.0 psi

\textbf{C.} 7.5 psi

\textbf{D.} More data is required to calculate this

Answer: A
Subdiscipline: structural

\textbf{Question 45:} A concrete mix design yields the following results:

Dry weight of coarse aggregate = 1,900 lb/yd\(^3\) \\
Water = 225 lb/yd\(^3\) \\
Dry weight of fine aggregate = 1,305 lb/yd\(^3\) \\
Dry weight of cement = 2.725 ft\(^3\)/yd\(^3\)

The coarse aggregate has in-situ moisture content of 2.5\% and absorption of 4.5\%. The fine aggregate has in-situ moisture content of 0.5\% and absorption of 2.5\%. The adjusted amount of water in lb/yd\(^2\) is most nearly:

\textbf{A.} 279

\textbf{B.} 289

\textbf{C.} 299

\textbf{D.} 311

Answer: B
Subdiscipline: construction

\textbf{Question 46:} A trapezoidal canal with side slopes of 3:4 on both sides, a depth of 12 feet, a bottom width of 10 feet, and a total length of 500 feet is to be lined with concrete for erosion control. The lining thickness is 6.0 in. all over the symmetric cross-section. With 10\% allowance for waste and over-excavation, the volume of concrete (yd\(^3\)) that must be delivered is most nearly:

\textbf{A.} 463

\textbf{B.} 510

\textbf{C.} 47

\textbf{D.} 575

Answer: B
Subdiscipline: geotechnical

\textbf{Question 47:} During the construction of a roadway, what kind of particles do not compact readily after applying a compaction roller?

\textbf{A.} Angular

\textbf{B.} Rounded

\textbf{C.} Flat and elongated

\textbf{D.} Smooth textured

Answer: A
Subdiscipline: structural

\textbf{Question 48:} The maximum bending stress occurs in a rectangular beam section and is most nearly:

\textbf{A.} At the neutral axis

\textbf{B.} At the extreme fiber

\textbf{C.} At a point where thickness is the minimum

\textbf{D.} None of the above

Answer: B
Subdiscipline: structural

\textbf{Question 49:} A drill rod with a diameter of 0.5 inches has a shear modulus of 12,000 ksi. The rod is subjected to a torque of \(T\). If the allowable shear stress of the rod is 40,000 psi, the minimum length of the rod so that one end of the rod rotates 10° with respect to the other is most nearly:

\textbf{A.} 9.1 in.

\textbf{B.} 10.1 in.

\textbf{C.} 11.1 in.

\textbf{D.} 13.1 in.

Answer: D
Subdiscipline: structural

\textbf{Question 50:} A steel pipe has a length of 6 ft, an outer diameter of 10 inches, and a wall thickness of 1.0 in. The Modulus of Elasticity of steel is 29,000 ksi and Poisson's Ratio is 0.30. If the pipe is subjected to an axial compression of 100 kip, a lateral strain of 0.0000366 occurs. The increase in thickness is most nearly:

\textbf{A.} 2.38 µ inch

\textbf{B.} 36.6 µ inch

\textbf{C.} 3.66 µ inch

\textbf{D.} 2.38 nano inch

Answer: B
Subdiscipline: structural

\textbf{Question 51:} A steel column is built-in at one end and free to translate and rotate at the other end. The column uses a 12 ft long W12 x 45 beam. If the yield strength of the steel is 50 kips/in\(^2\), the available design stress in the column is most nearly:

\textbf{Options:}

\begin{itemize} \item (A) 7.3 kips/in\(^2\) \item (B) 9.0 kips/in\(^2\) \item (C) 9.7 kips/in\(^2\) \item (D) 10 kips/in\(^2\) \end{itemize}

Answer: D
Subdiscipline: structural

\textbf{Question 52:} A 12-foot-long simply supported beam is subjected to a uniformly varying load that starts at 0 kip/ft at point A and increases linearly to 30 kip/ft at point B. What is the maximum moment in the beam?

\textbf{A.} 279 kipft

\textbf{B.} 186 kipft

\textbf{C.} 321 kipft

\textbf{D.} 0 kipft

Answer: A
Subdiscipline: structural

\textbf{Question 53:} What is the maximum deflection of a cantilever beam with a fixed end at one end and free at the other? It is 18 ft long and subjected to 3 kip/ft uniformly distributed load? \( E = 29 \times 10^3 \) ksi, \( I = 1,200 \) in\(^4\).

\textbf{A.} 0.90 in

\textbf{B.} 1.95 in

\textbf{C.} 2.35 in

\textbf{D.} 5.62 in

Answer: B
Subdiscipline: math

\textbf{Question 54:} A car is traveling along a path which can be expressed as \( r = 10 \theta^2 \), where \( \theta \) is in radians and \( r \) is in feet. If it runs at a speed of 30 ft/sec, what are the radial and transverse components of its velocity, respectively, when it travels at \( \theta = \frac{\pi}{2} \)?

\textbf{A.} 23.6, 18.5 ft/s

\textbf{B.} 21.6, 21.6 ft/s

\textbf{C.} 18.6, 16.3 ft/s

\textbf{D.} 12.3, 26.3 ft/s

Answer: A
Subdiscipline: math

\textbf{Question 55:} The angular acceleration of a 0.4-ft diameter circular disk can be represented as \[ \alpha = 5r^2 + 6t + 2 \text{ rad/sec}^{2}, \] where \( t \) is in seconds. The original angular velocity of the disk was 6 rad/sec, and after 5 sec, the angular velocity is 293.3 rad/s. The linear acceleration (ft/s\(^2\)) after 5 seconds of rotation is most nearly:

\textbf{A.} 31.4

\textbf{B.} 4,930

\textbf{C.} 13,005

\textbf{D.} 17,205

Answer: D
Subdiscipline: math

\textbf{Question 56:} A 1,000-kg block is to be rolled over a frictionless surface at a velocity of 0.1 m/s over a 0.6-m diameter frictionless pulley applying a tension. The kinetic energy (J) of the 12-kg pulley is most nearly:

\textbf{A.} 0.03

\textbf{B.} 0.3

\textbf{C.} 3.0

\textbf{D.} 30

Answer: A