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NYSTCE Physics study materials
NYSTCE Physics study resources

NYSTCE Physics practice questions

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Question 1Foundations of Scientific Inquiry

A student investigates how the angle of a ramp affects the speed of a cart at the bottom. In this experiment, which variable is the independent variable?

  1. The mass of the cart
  2. The angle of the ramp Correct answer.
  3. The length of the ramp
  4. The speed of the cart at the bottom

Explanation

The independent variable is the factor the experimenter deliberately changes. Here the ramp angle is manipulated, while the cart speed is measured as the dependent variable. Ramp length and cart mass should be held constant as controlled variables.

Question 2Foundations of Scientific Inquiry

A student measures a 50.00 g standard mass three times and records 49.02 g, 49.01 g, and 49.02 g. Which description best fits these measurements?

  1. Neither accurate nor precise
  2. Both accurate and precise
  3. Precise but inaccurate Correct answer.
  4. Accurate but imprecise

Explanation

Precision refers to how closely repeated measurements agree with one another, and these three values are very close together. Accuracy refers to closeness to the accepted value, and all three values are nearly 1 g below 50.00 g. The measurements are therefore precise but inaccurate.

Question 3Foundations of Scientific Inquiry

A graduated cylinder is marked in 1 mL increments. A student records a liquid volume as 42.0 mL. How many significant figures does this recorded value have?

  1. 3 Correct answer.
  2. 1
  3. 4
  4. 2

Explanation

In 42.0 mL, the digits 4 and 2 are nonzero and significant, and the trailing zero after the decimal point is also significant. The recorded value therefore has three significant figures. The decimal point matters because it makes the final zero a measured digit.

Question 4Foundations of Scientific Inquiry

A researcher tests a fertilizer by applying it to tomato plants in a greenhouse and applying no fertilizer to tomato plants outdoors. The fertilized plants yield more fruit. What is the most serious flaw in this design?

  1. Location was confounded with fertilizer treatment. Correct answer.
  2. She used an unnecessarily large number of plants.
  3. She did not include a no-fertilizer control group.
  4. She measured yield with insufficient precision.

Explanation

A valid experiment should differ between treatment and control groups only in the variable being tested. Here the fertilized plants are also in a different location, so greenhouse conditions such as temperature or light could explain the yield difference. Location is therefore a confounding variable.

Question 5Foundations of Scientific Inquiry

The accepted value of acceleration due to gravity is 9.81 m/s². A student's experiment gives 9.45 m/s². What is the percent error, rounded to one decimal place?

  1. 3.7% Correct answer.
  2. 0.037%
  3. 3.8%
  4. 0.37%

Explanation

Percent error is the absolute difference between experimental and accepted values, divided by the accepted value, times 100. The difference is 0.36 m/s², and 0.36 divided by 9.81 is about 0.0367. Multiplying by 100 gives about 3.7%.

Question 6Foundations of Scientific Inquiry

A graph plots an object's position on the vertical axis against time on the horizontal axis. For an object moving at constant velocity, the graph is a straight line. What does the slope of this line represent?

  1. Time
  2. Acceleration
  3. Velocity Correct answer.
  4. Displacement

Explanation

Slope is the change in the vertical quantity divided by the change in the horizontal quantity. For a position-time graph, that is change in position divided by change in time, which is velocity. A constant slope therefore indicates constant velocity.

Question 7Foundations of Scientific Inquiry

A speed is measured in kilometers per hour. Which operation correctly converts it to meters per second?

  1. Multiply by 1000 and by 3600
  2. Multiply by 1000 and divide by 3600 Correct answer.
  3. Divide by 1000 and by 3600
  4. Multiply by 3600 and divide by 1000

Explanation

One kilometer equals 1000 meters, and one hour equals 3600 seconds. Converting km/h to m/s therefore requires multiplying by 1000 and dividing by 3600. This is equivalent to multiplying by the conversion factor 1000/3600.

Question 8Foundations of Scientific Inquiry

A balance consistently reads 0.50 g too high for every mass placed on it, even though repeated readings are very close together. How should this measurement problem be classified?

  1. Systematic error that affects accuracy Correct answer.
  2. Human error that cannot be analyzed
  3. Random error with low precision
  4. Random error with high precision

Explanation

A consistent offset in the same direction is characteristic of systematic error, often caused by improper calibration. Because the repeated readings are close together, precision is high, but the offset makes the results inaccurate. Systematic error can often be corrected by recalibrating the instrument.

Question 9Foundations of Scientific Inquiry

A hypothesis predicts that raising temperature will increase a reaction rate. The rate does increase as temperature rises, but by much less than predicted. Which conclusion is most scientifically appropriate?

  1. The hypothesis must be rejected because the magnitude of change was wrong.
  2. The hypothesis is partly supported but needs quantitative refinement. Correct answer.
  3. The hypothesis is fully supported because the direction of change matched.
  4. The data are inconsistent with the hypothesis and should be discarded.

Explanation

The observed direction agrees with the prediction, so the hypothesis is not wholly contradicted. However, the much smaller magnitude shows that the quantitative part of the prediction is inadequate. Scientific conclusions should retain the supported portion while revising the model or hypothesis.

Question 10Foundations of Scientific Inquiry

A study finds a strong positive correlation between ice cream sales and drowning rates across the year. Which conclusion is most justified?

  1. Eating ice cream directly causes drowning in swimmers.
  2. Drowning directly causes increases in ice cream sales.
  3. A confounding variable may explain both. Correct answer.
  4. The correlation alone proves a direct causal relationship.

Explanation

Correlation measures association, not causation, so a strong relationship between two variables does not establish that one causes the other. A third variable such as seasonal temperature could increase both ice cream sales and swimming activity. Such a confounding variable can produce a misleading correlation.

Question 11Foundations of Scientific Inquiry

Which of the following is an SI base unit?

  1. kelvin Correct answer.
  2. newton
  3. joule
  4. liter

Explanation

The kelvin is one of the seven SI base units and is used to measure thermodynamic temperature. The newton and joule are derived units formed from base units, and the liter is a metric unit of volume that is not an SI base unit.

Question 12Foundations of Scientific Inquiry

A student measures the period of a pendulum five times and calculates the average. Averaging repeated measurements mainly reduces the effect of

  1. the true value of the pendulum period
  2. systematic error from a timer that runs slow
  3. the need to report units with the result
  4. random error from variable reaction time Correct answer.

Explanation

Random errors scatter above and below the true value, so averaging repeated trials tends to cancel their effects. A timer that consistently runs slow produces systematic error, which averaging cannot remove.

Question 13Foundations of Scientific Inquiry

A rectangular plate measures 2.5 cm by 3.42 cm. Applying significant-figure rules to the multiplication, which area should be reported?

  1. 9 cm²
  2. 8.55 cm²
  3. 8.6 cm² Correct answer.
  4. 8.550 cm²

Explanation

The value 2.5 cm has two significant figures, so the product must be rounded to two significant figures. The unrounded product is 8.55 cm², which rounds to 8.6 cm².

Question 14Foundations of Scientific Inquiry

A mineral sample has a density of 2.7 g/cm³. What is this density expressed in kg/m³?

  1. 27 kg/m³
  2. 2700 kg/m³ Correct answer.
  3. 0.0027 kg/m³
  4. 270 kg/m³

Explanation

One gram per cubic centimeter equals 1000 kilograms per cubic meter because 1 g = 0.001 kg and 1 cm³ = 10⁻⁶ m³. Multiplying 2.7 g/cm³ by 1000 gives 2700 kg/m³.

Question 15Foundations of Scientific Inquiry

In a double-blind trial of a new painkiller, neither the participants nor the researchers know who receives the drug and who receives a placebo. This design primarily minimizes

  1. random measurement error in the pain ratings
  2. the need for a control group in the trial
  3. variation caused by the participants' ages
  4. the placebo effect and experimenter bias Correct answer.

Explanation

Blinding prevents participants' expectations from producing placebo effects and prevents researchers from unconsciously influencing results or ratings. Random measurement error is reduced by repeated measurements and careful technique, not by blinding alone.

Question 16Foundations of Scientific Inquiry

During a laboratory investigation, one data point falls far from the pattern formed by the other trials. What is the most scientifically appropriate response?

  1. Move the point onto the line so the graph looks consistent
  2. Delete the point immediately and proceed without recording any reason
  3. Investigate the trial and document any reason before excluding it Correct answer.
  4. Discard the other points and analyze only the outlier

Explanation

An outlier should be investigated to determine whether it resulted from a known measurement error or a real effect. If it is excluded, the justification must be documented so the data analysis remains transparent and reproducible.

Question 17Foundations of Scientific Inquiry

Which statement is a falsifiable scientific hypothesis?

  1. Plants given 6 hours of light daily grow taller than plants given 3 hours daily. Correct answer.
  2. The night sky is considerably more beautiful and interesting than the daytime sky.
  3. There is an invisible, undetectable force that guides and controls all plant growth.
  4. Scientists should generally prefer one commercial fertilizer brand over another brand.

Explanation

A scientific hypothesis must make a testable prediction that could be shown to be false by observation or experiment. The statement about light duration predicts a measurable difference in plant height, so it can be tested and potentially disproved.

Question 18Foundations of Scientific Inquiry

A student adds two measured lengths: 12.3 cm ± 0.1 cm and 4.56 cm ± 0.02 cm. Applying the standard rule for addition, which reported result is correct?

  1. 16.86 cm ± 0.12 cm
  2. 16.9 cm ± 0.1 cm Correct answer.
  3. 16.8 cm ± 0.1 cm
  4. 17 cm ± 0.1 cm

Explanation

When measured values are added, their absolute uncertainties are added, giving 0.1 cm + 0.02 cm = 0.12 cm. The result 16.86 cm is then rounded to the same decimal place as the uncertainty, producing 16.9 cm ± 0.1 cm.

Question 19Foundations of Scientific Inquiry

A study reports that students who eat breakfast earn higher grades than students who skip breakfast. Which explanation is the strongest caution against concluding that breakfast causes higher grades?

  1. Grades are too difficult to measure accurately in any school setting.
  2. The study should have followed only one student for an entire school year.
  3. Breakfast foods vary widely in nutritional content and student preference.
  4. Family income may influence both breakfast habits and grades. Correct answer.

Explanation

An observed association may be produced by a confounding variable that affects both the suspected cause and the outcome. Family income could influence whether students eat breakfast and also affect academic performance, so the correlation alone does not establish causation.

Question 20Foundations of Scientific Inquiry

An experiment tests how substrate concentration affects the rate of an enzyme-catalyzed reaction. Which variable must be held constant to make the results valid?

  1. substrate concentration
  2. temperature Correct answer.
  3. reaction rate
  4. amount of product formed

Explanation

Temperature affects enzyme activity, so it must be kept the same across trials to isolate the effect of substrate concentration. Substrate concentration is the independent variable, while reaction rate and product amount are dependent measures.

Question 21Foundations of Scientific Inquiry

In an experiment testing a new study technique, which procedure best implements random assignment?

  1. Repeating the study in several different classrooms
  2. Measuring test scores with the same exam for all students
  3. Giving every student the same set of practice problems
  4. Assigning students to groups by a random process Correct answer.

Explanation

Random assignment means using chance to decide which participants enter each group, which helps make groups comparable on variables that could affect the outcome. Holding materials constant is a control procedure, while repeating the study in multiple classrooms is replication.

Question 22Foundations of Scientific Inquiry

In a controlled experiment, what is the primary purpose of a control group?

  1. To increase the total number of measurements
  2. To eliminate all random measurement error
  3. To keep the researchers unaware of the treatment
  4. To provide a baseline for comparison Correct answer.

Explanation

A control group receives no treatment or a standard treatment and supplies a reference point for judging the effect of the experimental treatment. It does not by itself increase sample size, remove random error, or create blinding.

Question 23Foundations of Scientific Inquiry

A hypothesis test yields a p-value of 0.04. Which interpretation is correct?

  1. There is a 4% probability that the null hypothesis is true.
  2. There is a 96% probability that the alternative hypothesis is true.
  3. Assuming the null, data this extreme occur 4% of the time. Correct answer.
  4. The probability that the result will replicate exactly is 4%.

Explanation

A p-value is the probability of obtaining results at least as extreme as those observed, assuming the null hypothesis is true. It is not the probability that the null or alternative hypothesis is true, and it is not a direct replication probability.

Question 24Foundations of Scientific Inquiry

A set of repeated measurements has a small standard deviation. What does this most directly indicate?

  1. The sample size is too small to analyze.
  2. The accepted value has been determined exactly.
  3. The measurements cluster near their mean. Correct answer.
  4. The measurements are all free of systematic error.

Explanation

Standard deviation measures the spread of repeated measurements around their mean, so a small value indicates that the measurements are close together, which is high precision. It does not by itself show absence of systematic error, exactness of the accepted value, or inadequacy of sample size.

Question 25Foundations of Scientific Inquiry

A graph plots force on the vertical axis against acceleration on the horizontal axis for an object of fixed mass. The slope of the line has units N/(m/s²). What does the slope represent?

  1. The mass of the object Correct answer.
  2. The acceleration of the object
  3. The velocity of the object
  4. The work done on the object

Explanation

Newton's second law gives F = ma, so a graph of force versus acceleration has slope m. The unit N/(m/s²) simplifies to kg, which is the unit of mass.

Question 26Foundations of Scientific Inquiry

Which practice most directly improves the reproducibility of an experiment?

  1. Reporting only the data that support the hypothesis
  2. Recording a detailed, step-by-step procedure Correct answer.
  3. Rounding all measurements to one significant figure
  4. Using more costly laboratory equipment

Explanation

Reproducibility requires enough methodological detail for another investigator to repeat the procedure and obtain comparable results. Equipment cost, selective reporting, and excessive rounding do not support that goal.

Question 27Foundations of Scientific Inquiry

A ruler is marked in 0.1 cm increments. Which recorded length is consistent with the ruler's precision?

  1. 4.567 cm
  2. 4.56 cm Correct answer.
  3. 4 cm
  4. 4.5 cm

Explanation

A measurement should include all certain digits plus one estimated digit. With 0.1 cm markings, the tenths digit is certain and the hundredths digit is estimated, so 4.56 cm is appropriate.

Question 28Foundations of Scientific Inquiry

A researcher's hypothesis predicts that increasing light intensity will raise the rate of photosynthesis, but the data show no significant change. What is the most appropriate next step?

  1. Revise or reject the hypothesis in light of the evidence Correct answer.
  2. Change the hypothesis after seeing the data and present it as original
  3. Claim that the hypothesis was supported anyway
  4. Discard the data because they contradict the hypothesis

Explanation

Scientific hypotheses are tentative explanations that must be evaluated against evidence. When results contradict a prediction, the appropriate response is to revise or reject the hypothesis, not to manipulate or misrepresent data.

Question 29Foundations of Scientific Inquiry

A linear graph fits data collected between 10 °C and 40 °C. A student uses the line to predict a value at 200 °C. What is the main risk in this prediction?

  1. Linear graphs cannot be used to make predictions.
  2. The prediction will have no units.
  3. The pattern may change outside the measured range. Correct answer.
  4. The original data must have been measured incorrectly.

Explanation

Extrapolation assumes that the fitted relationship continues beyond the observed range, which may be unjustified because the pattern could curve or change mechanism. It does not imply that the original data were wrong, that linear graphs are useless, or that units disappear.

Question 30Foundations of Scientific Inquiry

Two experiments test the same hypothesis. Experiment A uses 10 trials, and Experiment B uses 100 trials. Assuming similar variability, what is the most likely advantage of Experiment B?

  1. It gives a more reliable estimate of the true effect. Correct answer.
  2. It removes all systematic error from the measurements.
  3. It eliminates the need for a control group.
  4. It guarantees that the hypothesis is correct.

Explanation

A larger sample generally reduces the influence of random variation, making estimates more reliable and uncertainty intervals narrower. It does not replace a control group, guarantee a hypothesis, or eliminate systematic error.

Question 31Foundations of Scientific Inquiry

In the practice of physics, which description best characterizes a scientific theory?

  1. An untested speculation held by an individual researcher before publication
  2. A well-tested explanation that can be revised by new evidence Correct answer.
  3. A tentative prediction that has not yet been tested against measurements
  4. A summary statement that describes a consistent pattern without explaining it

Explanation

A scientific theory is a broad explanatory framework built from many confirmed results that unifies observations and predicts new ones; within science the word does not mean a guess. Because it must stay consistent with evidence, a theory is retained only while it survives testing and is modified or discarded when contradictory data accumulate. Its authority therefore comes from accumulated evidential support, not from the confidence of any single researcher.

Question 32Foundations of Scientific Inquiry

A student uses a digital thermometer that reads 1.5 °C too high for every sample, and the same offset appears in every trial. Which description of this measurement problem is correct?

  1. It is a rounding error, so recording one extra decimal place will eliminate it.
  2. It is a random error, so increasing the number of trials will reduce its effect.
  3. It is a precision limit, so the readings will scatter widely above and below the true value.
  4. It is a systematic error, so averaging repeated trials will not remove the offset. Correct answer.

Explanation

A systematic error shifts every reading in the same direction by the same amount, so it biases the mean instead of scattering it. Averaging cancels random fluctuations but leaves a constant offset fully intact, which is why the mean of many trials would still be 1.5 °C too high. Only calibration against a known standard, or subtracting the known offset, corrects this kind of error.

Question 33Foundations of Scientific Inquiry

A student determines the molar mass of a gas to be 57.6 g/mol. The accepted value is 60.0 g/mol. What is the student's percent error, expressed to the appropriate number of significant figures?

  1. 2.4%
  2. 4.0% Correct answer.
  3. 96.0%
  4. 4.2%

Explanation

Percent error is the absolute difference between the experimental and accepted values, divided by the accepted value and multiplied by 100. Here |57.6 − 60.0| = 2.4 g/mol, and 2.4 ÷ 60.0 × 100 = 4.0%, which carries two significant figures because the difference 2.4 has two. Only the size of the discrepancy is reported, so the result is usually given as a positive percentage.

Question 34Foundations of Scientific Inquiry

A student tests a fertilizer by growing 3 tomato plants with fertilizer in a sunlit greenhouse and 3 tomato plants without fertilizer in a shaded greenhouse. Which change would most directly remove the main threat to the validity of the comparison?

  1. Increase the number of plants in each group to thirty.
  2. Measure plant height instead of counting the number of tomatoes.
  3. Add fertilizer to the shaded group as well as to the sunlit group.
  4. Place both groups in the same greenhouse so that light exposure is identical. Correct answer.

Explanation

Fertilizer and light are varied together in this design, so any difference in yield could be attributed to either factor; light acts as a confounding variable that makes the fertilizer effect impossible to isolate. Equalizing light across groups, for instance by keeping all plants in one greenhouse and randomizing their positions, leaves fertilizer as the only systematic difference between the treatments. Larger samples or a different response variable may reduce noise or improve measurement, but they cannot disentangle two variables that change at once.

Question 35Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A ball is dropped from rest near Earth's surface, where air resistance is negligible. If g = 9.8 m/s², what is the ball's speed 3.0 s after release?

  1. 3.0 m/s
  2. 29 m/s Correct answer.
  3. 88 m/s
  4. 9.8 m/s

Explanation

For an object released from rest with negligible air resistance, speed increases linearly with time according to v = gt. Substituting g = 9.8 m/s² and t = 3.0 s gives v = 29.4 m/s, which rounds to 29 m/s.

Question 36Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A net force of 12 N acts on a 3.0 kg object. What is the magnitude of the object's acceleration?

  1. 9.0 m/s²
  2. 4.0 m/s² Correct answer.
  3. 0.25 m/s²
  4. 36 m/s²

Explanation

Newton's second law states that acceleration equals net force divided by mass, a = F_net/m. Dividing 12 N by 3.0 kg gives 4.0 m/s².

Question 37Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A uniform seesaw is balanced at its center. A 40 kg child sits 2.0 m to the left of the pivot. How far to the right of the pivot must an 80 kg child sit to balance the seesaw?

  1. 0.50 m
  2. 4.0 m
  3. 1.0 m Correct answer.
  4. 2.0 m

Explanation

For a balanced seesaw, the torques on each side of the pivot must be equal in magnitude: m₁r₁ = m₂r₂. Solving 40 kg × 2.0 m = 80 kg × r₂ gives r₂ = 1.0 m.

Question 38Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A 5.0 kg crate slides 4.0 m across a horizontal floor. The coefficient of kinetic friction between crate and floor is 0.30. How much work does friction do on the crate? (g = 9.8 m/s²)

  1. −20 J
  2. −59 J Correct answer.
  3. 0 J
  4. +59 J

Explanation

The work done by kinetic friction is W = −f_k d = −μ_k mg d because friction opposes the displacement. Substituting μ_k = 0.30, m = 5.0 kg, g = 9.8 m/s², and d = 4.0 m gives about −59 J.

Question 39Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A 2.0 kg cart moving at 4.0 m/s collides with and sticks to a 3.0 kg cart that is initially at rest on a frictionless track. What is the speed of the combined carts immediately after the collision?

  1. 2.7 m/s
  2. 1.6 m/s Correct answer.
  3. 4.0 m/s
  4. 2.0 m/s

Explanation

In a perfectly inelastic collision, momentum is conserved but kinetic energy is not. The total momentum before is (2.0 kg)(4.0 m/s) = 8.0 kg·m/s, and dividing by the combined mass of 5.0 kg gives 1.6 m/s.

Question 40Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A car travels around a flat, unbanked curve of radius 50 m. The coefficient of static friction between the tires and the road is 0.40. What is the maximum speed the car can have without skidding? (g = 9.8 m/s²)

  1. 7.0 m/s
  2. 28 m/s
  3. 20 m/s
  4. 14 m/s Correct answer.

Explanation

On a flat curve, static friction provides the centripetal force, so μ_s mg = mv²/r. Solving v = √(μ_s g r) with μ_s = 0.40, g = 9.8 m/s², and r = 50 m gives v ≈ 14 m/s.

Question 41Mechanics (kinematics, dynamics, energy, momentum, gravitation)

Two satellites orbit Earth in circular orbits. Satellite A has orbital radius r, and satellite B has orbital radius 4r. What is the ratio of A's orbital period to B's orbital period?

  1. 1:4
  2. 1:16
  3. 1:8 Correct answer.
  4. 1:2

Explanation

Kepler's third law states that T² is proportional to r³ for circular orbits, so T scales as r^(3/2). The radius ratio is 1:4, and (1/4)^(3/2) = 1/8, giving a period ratio of 1:8.

Question 42Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A ball is thrown horizontally at 15 m/s from a cliff 20 m high. How far from the base of the cliff does it land? (Ignore air resistance; g = 9.8 m/s²)

  1. 20 m
  2. 45 m
  3. 30 m Correct answer.
  4. 15 m

Explanation

The vertical motion determines the fall time: h = ½gt², so t = √(2h/g). With h = 20 m and g = 9.8 m/s², t ≈ 2.0 s, and the horizontal range is x = v_x t = (15 m/s)(2.0 s) ≈ 30 m.

Question 43Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A car starts from rest and accelerates uniformly at 2.0 m/s². At the same instant, a truck traveling at a constant 16 m/s passes the car. How long does it take the car to catch the truck?

  1. 32 s
  2. 8.0 s
  3. 16 s Correct answer.
  4. 4.0 s

Explanation

The car's displacement is ½at² = (1.0 m/s²)t², while the truck's displacement is (16 m/s)t. Setting them equal gives t² = 16t, so t = 16 s (the nonzero solution).

Question 44Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A 2.0 kg block slides from rest down a frictionless ramp and then compresses a spring at the bottom. The block starts 1.8 m above the bottom of the ramp. The spring has a spring constant of 800 N/m. What is the maximum compression of the spring? (g = 9.8 m/s²)

  1. 0.42 m
  2. 0.21 m
  3. 0.30 m Correct answer.
  4. 0.60 m

Explanation

Mechanical energy is conserved on the frictionless ramp and during ideal spring compression: mgh = ½kx². Solving for x gives x = √(2mgh/k) = √(2 × 2.0 × 9.8 × 1.8 / 800) ≈ 0.30 m.

Question 45Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A cyclist traveling at 8.0 m/s applies the brakes and comes to rest with constant acceleration in 4.0 s. What distance does the cyclist travel during braking?

  1. 32 m
  2. 64 m
  3. 16 m Correct answer.
  4. 8.0 m

Explanation

For constant acceleration, the average velocity is (8.0 m/s + 0)/2 = 4.0 m/s, so the distance is (4.0 m/s)(4.0 s) = 16 m. Equivalently, the acceleration is −2.0 m/s², and x = v_i t + ½at² gives the same result.

Question 46Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A book rests on a table. Earth exerts a downward gravitational force on the book. According to Newton's third law, which force is the paired reaction to that gravitational force?

  1. The normal force the table exerts on the book
  2. The normal force the book exerts on the table
  3. The net force on the book, which is zero
  4. The gravitational force the book exerts on Earth Correct answer.

Explanation

Newton's third-law pairs act on different objects, have the same type, and are opposite in direction. The reaction to Earth pulling the book downward is therefore the book pulling Earth upward, not a contact force from the table.

Question 47Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A 2.0 kg object is raised vertically 3.0 m at constant speed near Earth's surface. Taking g = 9.8 m/s², by how much does the object's gravitational potential energy increase?

  1. 59 J Correct answer.
  2. 29 J
  3. 120 J
  4. 6.0 J

Explanation

The work done in lifting at constant speed equals the increase in gravitational potential energy, ΔU = mgΔh = (2.0 kg)(9.8 m/s²)(3.0 m) = 58.8 J, which rounds to 59 J.

Question 48Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A 0.20 kg ball strikes a wall horizontally at 12 m/s and rebounds horizontally at 8.0 m/s. If the ball and wall are in contact for 0.040 s, what is the magnitude of the average force the wall exerts on the ball?

  1. 20 N
  2. 100 N Correct answer.
  3. 40 N
  4. 200 N

Explanation

Choose the initial direction as positive. The change in momentum is Δp = m(v_f − v_i) = (0.20 kg)(−8.0 − 12) m/s = −4.0 kg·m/s. The average force magnitude is |Δp|/Δt = 4.0/0.040 = 100 N.

Question 49Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A 60 kg student climbs a vertical rope 5.0 m at a constant speed in 10 s. What is the student's average power output?

  1. 290 W Correct answer.
  2. 2900 W
  3. 590 W
  4. 30 W

Explanation

At constant speed, the student's work goes into increasing gravitational potential energy. Average power is P = mgh/t = (60 kg)(9.8 m/s²)(5.0 m)/(10 s) ≈ 294 W, or about 290 W.

Question 50Mechanics (kinematics, dynamics, energy, momentum, gravitation)

A 0.50 kg ball on a string moves in a vertical circle of radius 0.80 m. At the top of the circle, its speed is 3.0 m/s. What is the tension in the string at that point? (Use g = 9.8 m/s².)

  1. 0 N
  2. 5.6 N
  3. 0.73 N Correct answer.
  4. 10 N

Explanation

At the top of the circle, both tension and weight point toward the center, so T + mg = mv²/r. Solving gives T = (0.50)(3.0)²/0.80 − (0.50)(9.8) = 5.625 − 4.9 ≈ 0.73 N.