This question tests understanding that net force and acceleration are directly proportional, as described by Newton's Second Law: F_net = ma. The data show a direct proportional relationship between net force and acceleration: when net force increases, acceleration increases by the same factor (double the force → double the acceleration), and when net force decreases, acceleration decreases proportionally—this relationship is linear, meaning if you graph F_net (x-axis) vs acceleration (y-axis), you get a straight line through the origin, and the slope of that line equals 1/m (the reciprocal of the object's mass). This proportionality is Newton's Second Law: F_net = ma, which can be rearranged to a = F_net/m, showing that for constant mass, acceleration is directly proportional to net force. Looking at the data: when net force is 5 N, acceleration is 2.5 m/s², when net force increases to 10 N (doubled), acceleration increases to 5.0 m/s² (also doubled), and when net force increases further to 15 N (tripled from original), acceleration is 7.5 m/s² (also tripled)—this consistent doubling and tripling demonstrates perfect proportionality. The ratio F_net/a is constant throughout: 5/2.5 = 2, 10/5 = 2, 15/7.5 = 2 (this constant ratio equals the object's mass m = 2 kg in this example), confirming Newton's Second Law F_net = ma holds for all data points. Choice A is correct because it properly recognizes the linear pattern in graph or constant ratio in table / correctly predicts that increasing net force will proportionally increase acceleration, so for 20 N (double 10 N or quadruple 5 N), a = 10 m/s² (double 5 or quadruple 2.5). Choice B is wrong because it suggests there's no relationship or that acceleration is independent of force, when the data clearly show acceleration changes systematically with net force / makes incorrect prediction: claims doubling force would triple or halve acceleration, when proportionality means doubling force doubles acceleration. Collecting and analyzing force-motion data: (1) set up investigation with constant mass object, (2) apply different net forces (use force sensor or known applied force minus friction), (3) measure resulting acceleration for each force (motion sensor, or calculate from distance and time), (4) record data in table: F_net | a values, (5) graph data: F_net on x-axis, a on y-axis, (6) analyze pattern: should see straight line through origin showing proportionality, (7) calculate slope: slope = Δa/ΔF_net = 1/m, allows determining object's mass from the data. Real investigations might show slight deviations from perfect line (measurement uncertainty, friction variations), but overall pattern should be clear: larger net forces produce larger accelerations proportionally—this relationship F_net = ma is one of the most fundamental in physics, describing how forces cause motion changes in everything from tiny molecules to planets, and collecting data to verify it experimentally (as students can do with carts, ramps, and force sensors) demonstrates how physics laws are not just theoretical but are actually observed patterns in nature that we can measure and test.

This question tests understanding that net force and acceleration are directly proportional, as described by Newton's Second Law: F_net = ma. The data show a direct proportional relationship between net force and acceleration: when net force increases from 0 to 5 to 10 to 15 N, acceleration increases from 0 to 2.5 to 5.0 to 7.5 m/s²—each time force doubles (5→10 N), acceleration also doubles (2.5→5.0 m/s²), and the ratio F_net/a remains constant at 2 throughout all non-zero data points. Looking at the data more closely: 5/2.5 = 2, 10/5.0 = 2, 15/7.5 = 2, confirming that F_net = 2a, which means the cart's mass is 2 kg (since F_net = ma, so m = F_net/a = 2 kg). Choice C is correct because it accurately identifies the proportional relationship: doubling F_net doubles a, which is exactly what the data show—when force goes from 5 to 10 N (doubled), acceleration goes from 2.5 to 5.0 m/s² (also doubled). Choice A is wrong because it claims an inverse relationship (larger force → smaller acceleration) when the data clearly show both increasing together; Choice B incorrectly states acceleration stays constant when it clearly changes from 0 to 7.5 m/s²; Choice D suggests a nonlinear squared relationship when the data form a perfect straight line through the origin. To investigate this relationship experimentally: (1) use a low-friction track and cart of known mass, (2) apply measured forces using spring scales or hanging masses, (3) measure acceleration using motion sensors or from distance-time data, (4) plot F_net vs a to verify the linear relationship—this fundamental experiment demonstrates Newton's Second Law applies to all objects, from lab carts to rockets.

This question tests understanding that net force and acceleration are directly proportional, as described by Newton's Second Law: F_net = ma. The data show a direct proportional relationship between net force and acceleration: when net force increases, acceleration increases by the same factor (double the force → double the acceleration), and when net force decreases, acceleration decreases proportionally—this relationship is linear, meaning if you graph F_net (x-axis) vs acceleration (y-axis), you get a straight line through the origin, and the slope of that line equals 1/m (the reciprocal of the object's mass). This proportionality is Newton's Second Law: F_net = ma, which can be rearranged to a = F_net/m, showing that for constant mass, acceleration is directly proportional to net force. Looking at the data: when net force is 5 N, acceleration is 2.5 m/s², when net force increases to 10 N (doubled), acceleration increases to 5.0 m/s² (also doubled), and when net force increases further to 15 N (tripled from original), acceleration is 7.5 m/s² (also tripled)—this consistent doubling and tripling demonstrates perfect proportionality. The ratio F_net/a is constant throughout: 5/2.5 = 2, 10/5 = 2, 15/7.5 = 2 (this constant ratio equals the object's mass m = 2 kg in this example), confirming Newton's Second Law F_net = ma holds for all data points. The straight line through the origin shows the proportional relationship clearly—the graph passes through (0,0) because zero net force produces zero acceleration (balanced forces), and increases linearly showing each additional Newton of force produces a consistent amount of additional acceleration. Choice B is correct because it accurately identifies the proportional relationship: F_net ∝ a or F_net = ma / correctly interprets the data showing that doubling force doubles acceleration / properly recognizes the linear pattern in graph or constant ratio in table / correctly predicts that increasing net force will proportionally increase acceleration. Choice A is wrong because it claims an inverse relationship (larger force → smaller acceleration) when the data clearly show the opposite: as force increases from 5 N to 10 N to 15 N, acceleration increases from 2.5 to 5.0 to 7.5 m/s² (both increase together). Collecting and analyzing force-motion data: (1) set up investigation with constant mass object, (2) apply different net forces (use force sensor or known applied force minus friction), (3) measure resulting acceleration for each force (motion sensor, or calculate from distance and time), (4) record data in table: F_net | a values, (5) graph data: F_net on x-axis, a on y-axis, (6) analyze pattern: should see straight line through origin showing proportionality, (7) calculate slope: slope = Δa/ΔF_net = 1/m, allows determining object's mass from the data. Real investigations might show slight deviations from perfect line (measurement uncertainty, friction variations), but overall pattern should be clear: larger net forces produce larger accelerations proportionally—this relationship F_net = ma is one of the most fundamental in physics, describing how forces cause motion changes in everything from tiny molecules to planets, and collecting data to verify it experimentally (as students can do with carts, ramps, and force sensors) demonstrates how physics laws are not just theoretical but are actually observed patterns in nature that we can measure and test.

This question tests understanding that net force and acceleration are directly proportional, as described by Newton's Second Law: F_net = m a. The data show a direct proportional relationship between net force and acceleration: when net force increases, acceleration increases by the same factor (double the force → double the acceleration), and when net force decreases, acceleration decreases proportionally—this relationship is linear, meaning if you graph F_net (x-axis) vs acceleration (y-axis), you get a straight line through the origin, and the slope of that line equals 1/m (the reciprocal of the object's mass). Looking at the data: when net force is 5 N, acceleration is 2.5 m/s²; when net force increases to 10 N (doubled), acceleration increases to 5.0 m/s² (also doubled); and when net force increases further to 15 N (tripled from original), acceleration is 7.5 m/s² (also tripled)—this consistent doubling and tripling demonstrates perfect proportionality. The ratio F_net/a is constant throughout: 5/2.5=2, 10/5=2, 15/7.5=2 (this constant ratio equals the object's mass m=2 kg), confirming Newton's Second Law F_net = m a holds for all data points. Choice B is correct because it accurately identifies the proportional relationship: acceleration increases with net force in a direct proportion, and doubling F_net doubles a. Choice A is wrong because it claims an inverse relationship (larger force → smaller acceleration) when the data clearly show the opposite: as force increases from 5 N to 10 N to 15 N, acceleration increases from 2.5 to 5.0 to 7.5 m/s². Collecting and analyzing force-motion data: (1) set up investigation with constant mass object, (2) apply different net forces (use force sensor or known applied force minus friction), (3) measure resulting acceleration for each force (motion sensor, or calculate from distance and time), (4) record data in table: F_net | a values, (5) graph data: F_net on x-axis, a on y-axis, (6) analyze pattern: should see straight line through origin showing proportionality, (7) calculate slope: slope = Δa/ΔF_net = 1/m, allows determining object's mass from the data.

This question tests understanding that net force and acceleration are directly proportional, as described by Newton's Second Law: F_net = m a. The data show a direct proportional relationship between net force and acceleration: when net force increases, acceleration increases by the same factor (double the force → double the acceleration)—this relationship is linear, with constant mass implied by the constant ratio F_net / a = 5 kg (e.g., 2/0.4=5, 4/0.8=5, 6/1.2=5). Looking at the data: when net force doubles from 2 N to 4 N, acceleration doubles from 0.4 m/s² to 0.8 m/s²—this consistent doubling demonstrates perfect proportionality. Choice B is correct because it accurately identifies that acceleration doubles when net force doubles, matching the data's proportional pattern. Choice A is wrong because it claims acceleration is cut in half (larger force → smaller acceleration) when the data clearly show the opposite: as force increases, acceleration increases proportionally. Collecting and analyzing force-motion data: (1) set up investigation with constant mass object, (2) apply different net forces (use force sensor or known applied force minus friction), (3) measure resulting acceleration for each force (motion sensor, or calculate from distance and time), (4) record data in table: F_net | a values, (5) graph data: F_net on x-axis, a on y-axis, (6) analyze pattern: should see straight line through origin showing proportionality, (7) calculate slope: slope = Δa/ΔF_net = 1/m, allows determining object's mass from the data.

This question tests understanding that net force and acceleration are directly proportional, as described by Newton's Second Law: F_net = m a, and how this affects distance traveled via d = (1/2) a t² for constant time. The data show a direct proportional relationship between net force and acceleration: since a = F_net / m, distance d = (1/2) (F_net / m) t², so d is proportional to F_net for fixed t and m. Looking at the data: for 5 N, a=2.5 m/s², d=(1/2)2.54=5 m; for 15 N, a=7.5 m/s², d=(1/2)7.54=15 m—the difference is 15-5=10 m, showing tripling force triples acceleration and thus triples distance. Choice B is correct because it correctly calculates the difference in distance as 10 m, based on the proportional relationship and the formula d=(1/2) a t². Choice A is wrong because it gives 5 m, perhaps calculating only the distance for 5 N or misapplying the formula without finding the difference. Collecting and analyzing force-motion data: (1) set up investigation with constant mass object, (2) apply different net forces (use force sensor or known applied force minus friction), (3) measure resulting acceleration for each force (motion sensor, or calculate from distance and time), (4) record data in table: F_net | a values, (5) graph data: F_net on x-axis, a on y-axis, (6) analyze pattern: should see straight line through origin showing proportionality, (7) calculate slope: slope = Δa/ΔF_net = 1/m, allows determining object's mass and predicting outcomes like distance differences.

This question tests understanding that net force and acceleration are directly proportional, as described by Newton's Second Law: F_net = m a, and how to design a fair experiment to verify this. To show the relationship, keep mass constant (same cart) and vary only F_net while measuring a—this isolates the effect of force on acceleration, ensuring a fair test. The best plan involves applying different measured net forces to the same cart and recording accelerations, allowing observation of the proportional pattern (e.g., doubling F_net doubles a). Choice A is correct because it uses the same cart each time, applies several different measured net forces, and records acceleration, which fairly tests the F_net-a relationship with controlled variables. Choice B is wrong because it changes to a heavier cart each time (varying mass) while keeping force the same, which would show mass's effect instead of force's, not isolating the F_net-a proportionality. Collecting and analyzing force-motion data: (1) set up investigation with constant mass object, (2) apply different net forces (use force sensor or known applied force minus friction), (3) measure resulting acceleration for each force (motion sensor, or calculate from distance and time), (4) record data in table: F_net | a values, (5) graph data: F_net on x-axis, a on y-axis, (6) analyze pattern: should see straight line through origin showing proportionality, (7) calculate slope: slope = Δa/ΔF_net = 1/m, allows determining object's mass from the data.

This question tests understanding that net force and acceleration are directly proportional, as described by Newton's Second Law: F_net = m a, and since Δv = a Δt with fixed Δt, Δv is also proportional to F_net. The data show a direct proportional relationship between net force and change in speed: when net force doubles from 4 N to 8 N, Δv doubles from 1 to 2 m/s, and to 12 N (tripled from 4 N), Δv triples to 3 m/s—this linear pattern confirms Δv ∝ F_net for constant m and Δt. Looking at the data: the ratio F_net / Δv is constant at 4/1=4, 8/2=4, 12/3=4 (this relates to m / Δt, since Δv = (F_net / m) Δt), verifying the proportionality. Choice A is correct because it accurately describes the proportional relationship: as F_net increases, Δv increases in direct proportion, with doubling force giving double the speed change. Choice B is wrong because it claims Δv decreases as F_net increases, but the data show the opposite: Δv increases with F_net, not inversely. Collecting and analyzing force-motion data: (1) set up investigation with constant mass object, (2) apply different net forces (use force sensor or known applied force minus friction), (3) measure resulting acceleration for each force (motion sensor, or calculate from distance and time), (4) record data in table: F_net | a values, (5) graph data: F_net on x-axis, a on y-axis, (6) analyze pattern: should see straight line through origin showing proportionality, (7) calculate slope: slope = Δa/ΔF_net = 1/m, allows determining object's mass and extending to Δv predictions.

This question tests understanding that net force and acceleration are directly proportional, as described by Newton's Second Law: F_net = m a, and how this connects to change in velocity via Δv = a Δt for constant time. The data show a direct proportional relationship between net force and acceleration: for constant mass, a = F_net / m, so Δv = (F_net / m) Δt, meaning Δv is also proportional to F_net when Δt is fixed. Looking at the data: for 5 N, a=2.5 m/s², Δv=2.52=5 m/s; for 10 N, a=5.0 m/s² (doubled), so Δv=5.02=10 m/s (also doubled)—this demonstrates the proportionality extends to velocity change. Choice C is correct because it correctly calculates Δv = a Δt = 5.0 * 2 = 10 m/s for F_net=10 N, matching the pattern where doubling force doubles acceleration and thus doubles Δv. Choice B is wrong because it suggests 5.0 m/s, perhaps confusing Δv with a itself or using the wrong time, but the formula clearly gives 10 m/s. Collecting and analyzing force-motion data: (1) set up investigation with constant mass object, (2) apply different net forces (use force sensor or known applied force minus friction), (3) measure resulting acceleration for each force (motion sensor, or calculate from distance and time), (4) record data in table: F_net | a values, (5) graph data: F_net on x-axis, a on y-axis, (6) analyze pattern: should see straight line through origin showing proportionality, (7) calculate slope: slope = Δa/ΔF_net = 1/m, allows determining object's mass from the data and predicting motion changes like Δv.

This question tests understanding that net force and acceleration are directly proportional, as described by Newton's Second Law: F_net = m a, allowing prediction of acceleration for new forces based on the pattern. The data show a direct proportional relationship between net force and acceleration: when net force doubles from 5 N to 10 N, acceleration doubles from 2.5 to 5.0 m/s², and from 5 N to 15 N (tripled), acceleration triples to 7.5 m/s²—this linear pattern means a = F_net / m, with m constant. Looking at the data: the ratio F_net/a is constant at 5/2.5=2, 10/5=2, 15/7.5=2, so m=2 kg; for 20 N, a = 20 / 2 = 10 m/s², following the same proportionality. Choice A is correct because it properly predicts that increasing net force to 20 N (quadrupled from 5 N) will quadruple the acceleration to 10 m/s², consistent with the linear pattern in the table. Choice B is wrong because it suggests 8 m/s², which would not fit the constant ratio (20/8=2.5, but data show 2); it miscalculates the pattern, perhaps confusing with a different mass or non-linear relationship. Collecting and analyzing force-motion data: (1) set up investigation with constant mass object, (2) apply different net forces (use force sensor or known applied force minus friction), (3) measure resulting acceleration for each force (motion sensor, or calculate from distance and time), (4) record data in table: F_net | a values, (5) graph data: F_net on x-axis, a on y-axis, (6) analyze pattern: should see straight line through origin showing proportionality, (7) calculate slope: slope = Δa/ΔF_net = 1/m, allows determining object's mass from the data and predicting for new forces.