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B2.6 · Plan an inquiry into one-dimensional motion

Learn to plan an inquiry into one-dimensional motion through clear examples and targeted practice.

Ontario Grade 11 Physics

Kinematics

Turn a motion question into a fair, safe, and useful investigation

An inquiry is a planned investigation that uses observations or measurements to answer a question. In one-dimensional motion, an object moves along one straight line. A useful plan states what will move, what will be measured, how the measurements will be made, and how the evidence will answer the question. This lesson focuses on planning. Proposed procedures and predicted values below are not results from a completed experiment.

What you will learn

Describe the system and choose a positive direction for an inquiry into motion along one straight line.
Plan how to measure position and time, and identify variables that should be kept consistent.
Choose a suitable way to record and compare motion observations.
Use a motion relationship to make a prediction and check that its units and direction make sense.

1. Start with the motion and a clear question

First define the system. The system is the object or group of objects being studied. For example, a cart rolling along a straight track can be the system. Decide what position means: position is the object's location compared with a chosen reference point. A metre (m) is the SI unit for position.

Choose a reference frame: the reference frame is the viewpoint and reference point used to describe motion. For a track investigation, the track can be the reference frame and one end can be the zero position. Choose one direction along the track as positive. Positions in the opposite direction are negative. State this choice before collecting data.

Distance is a scalar: it has size but no direction. Displacement is a vector: it has size and direction. In one dimension, a displacement can be shown with a positive or negative sign once the positive direction is chosen. Do not use the words as if they mean the same thing.

A focused inquiry question names a factor to change or compare and an outcome to observe. For instance: “How does the release position affect the cart’s position after a fixed time?” This is more useful than “What happens to the cart?” because it identifies a comparison and a measurable result.

Name the system, reference point, reference frame, and positive direction.
Make the question specific enough to guide measurements.
Use signs to show direction; a sign does not change a vector into a scalar.

2. Choose measurements and plan a fair test

A variable is a quantity that can change. The independent variable is the factor deliberately changed. The dependent variable is the result measured. Controlled variables are factors kept the same so the comparison is fair. In the cart question, release position could be independent, position after a fixed time could be dependent, and the cart, track, timing interval, and release method could be controlled.

Position and time are central measurements for describing one-dimensional motion. Record position in metres and elapsed time in seconds (s). A position-time record pairs each time with the object's position. A motion graph can display time on the horizontal axis and position on the vertical axis. Label both axes with quantities and units, and show the chosen positive direction in the plan.

Plan how each reading will be made. Identify the measuring tool, the start and end points for timing, and how the object will be released. Use the same method each time. If a person starts a stopwatch by hand, reaction time can make timing less consistent. A plan should acknowledge such limits and, when practical, repeat each condition and compare the readings rather than relying on one trial.

Decide what evidence would answer the question before collecting it. For example, compare the measured position at the same elapsed time for each release position. Record observations in a labelled table. Do not change several factors at once, because then the cause of a difference is unclear. Include safety steps that fit the setup, such as securing the track and keeping the path clear.

Identify independent, dependent, and controlled variables.
State measurement tools, units, timing method, and repeat plan.
Decide in advance how the recorded evidence will be compared.

3. Connect the plan to a simple motion model

A model is a simplified way to describe or predict a situation. For motion over a stated time interval, average velocity is displacement divided by elapsed time. Velocity is a vector, so its sign shows direction. The symbol

\Delta x

means change in position, and

\Delta t

means elapsed time. Use metres, seconds, and metres per second (m/s).

A predicted value can help check whether a proposed timing interval or measuring range is suitable. A prediction is not measured evidence. In a real inquiry, measurements would be recorded and compared with the prediction. If the expected motion is too small to distinguish with the chosen measuring method, revise the plan before starting.

A labelled position-time graph can help organize the plan: horizontal axis, elapsed time

t

(s); vertical axis, position

x

(m); positive position in the chosen direction. Planned observations would appear as points only after measurements are made. Do not draw invented points and present them as experimental results.

\bar{v}=\frac{\Delta x}{\Delta t}

Use a model to guide a plan, not to claim that measurements have occurred.
Keep units and direction consistent in predictions and records.
A graph needs labelled axes and units; its points must come from identified evidence.

4. Review and improve the inquiry plan

Before carrying out an inquiry, check that the procedure can answer the question. Each step should say what is changed, what is measured, and what is kept consistent. Check that the measuring range suits the expected motion and that the units are recorded. A clear plan also says how many repeats are intended and how observations will be compared.

Measured evidence is information gathered by carrying out the procedure. A prediction is a value expected from a model. A simulated result comes from a computer representation. These are different kinds of information. A plan may propose a simulation, but it must not describe simulated output as a physical measurement.

A useful final review asks: Is the system clear? Is the positive direction stated? Can another student follow the method? Are the variables and units clear? Is the comparison fair? Is the procedure safe? If any answer is no, revise the plan before collecting evidence.

Separate predictions, measurements, and simulated output.
Make the procedure repeatable and safe.
Check that the chosen observations answer the original question.

Worked example

Example 1: Make a broad question testable

A student wants to investigate a cart moving along a straight track. Improve the question and identify the system, direction, and main variables.

Define the motion
Treat the cart as the system and the track as the reference frame. Choose the direction from the track's marked zero end toward the far end as positive.
Specify the comparison
A testable question is: “How does the cart’s release position affect its position after 2.0 s?” Release position is the independent variable. Position after 2.0 s is the dependent variable.
Name controls
Keep the same cart, track, timing interval, and release method. Record position in metres and time in seconds. These choices make the comparison more consistent.

Answer: The plan studies a cart on a straight track, with motion toward the far end defined as positive. It compares release position with position after a fixed elapsed time.

Check: The question identifies a changed factor and a measurable outcome. The positive direction is explicit, so position signs can be interpreted.

Worked example

Example 2: Check whether a proposed timing interval is suitable

For planning only, suppose a cart is expected to travel about 0.80 m in 2.0 s in the positive direction. Estimate its average velocity to help choose a position-measuring range. These are predicted values, not experimental data.

Set the direction and known values
The system is the cart, and the positive direction is along the track toward the far end. The proposed displacement is positive, and the elapsed time is positive.
$\Delta x=+0.80\,\mathrm{m},\quad \Delta t=2.0\,\mathrm{s}$
Use the motion relationship
Average velocity is displacement divided by elapsed time. The units reduce to metres per second, which is the SI unit for velocity.
$\bar{v}=\frac{\Delta x}{\Delta t}=\frac{+0.80\,\mathrm{m}}{2.0\,\mathrm{s}}=+0.40\,\mathrm{m/s}$
Check the prediction
The positive sign means the predicted motion is toward the far end. Two significant figures match the given values. A range that includes the expected 0.80 m displacement would be suitable to consider.

Answer: The predicted average velocity is

+0.40\,\mathrm{m/s}

, toward the far end of the track.

Check: The units are m/s, the sign agrees with the chosen direction, and a speed of 0.40 m/s for 2.0 s gives a displacement of 0.80 m. This is a planning estimate, not a measured result.

Worked example

Example 3: Plan a comparison of two motion conditions

Plan an inquiry comparing how far a toy car travels in a fixed time when released from two different starting positions on a straight, level path.

Set the system and direction
The toy car is the system. Use the floor path as the reference frame, mark a zero position, and define motion away from zero as positive.
Plan the procedure
Choose two marked starting positions. Use the same car, path, release method, and time interval for both conditions. Measure the car’s position at the chosen elapsed time using a metre ruler or tape. Repeat each condition if practical.
Record and compare evidence
Make a table with condition, elapsed time in seconds, and position in metres. Compare positions at the same elapsed time. Treat the readings as measured evidence only after the procedure is carried out; do not fill the table with guessed results.

Answer: The plan changes starting position, measures position after a fixed time, and controls the car, path, release method, and timing interval.

Check: The comparison uses the same outcome and time interval in both conditions. Position has a stated reference and positive direction, and no result is claimed before measurement.

Common mistakes and how to avoid them

Using “distance” when the plan actually needs position or displacement.

Correction: Distance has no direction. Position is relative to a reference point, and displacement includes direction. State which one is being recorded.

Changing the release point, cart, and timing method at the same time.

Correction: Change the intended independent variable while keeping other relevant conditions consistent. Otherwise, a difference cannot be linked clearly to one factor.

Treating a predicted value or a computer output as a physical measurement.

Correction: Label predictions and simulated results clearly. Call information measured evidence only when it is gathered through the stated measurement procedure.

Recording numbers without units or a positive direction.

Correction: Write units with every recorded quantity and state the direction convention. This makes values interpretable and comparable.

Lesson summary

Define the system, reference frame, reference point, and positive direction before planning measurements.
Write a focused question and identify the independent, dependent, and controlled variables.
Plan a repeatable method for measuring position and time, with SI units and suitable records.
Use a motion relationship to make a clearly labelled prediction, then check its units, sign, and reasonableness.
Keep measured evidence distinct from predictions and simulated results.

Check your understanding

Question 1

A cart moves along a track. Which plan best identifies a dependent variable for the question “How does release position affect the cart’s motion after 1.5 s?”

The cart used in the inquiry
The cart’s position after 1.5 s
The direction chosen as positive
The track surface kept unchanged

Show answer and explanation

The cart’s position after 1.5 s

The dependent variable is the outcome measured. Here it is the cart’s position after the fixed time.

Question 2

A student defines rightward as positive and records a displacement of

-0.30\,\mathrm{m}

. What does the sign indicate?

The object moved leftward by 0.30 m
The object moved rightward by 0.30 m
The object travelled for 0.30 s
The object has a mass of 0.30 kg

Show answer and explanation

The object moved leftward by 0.30 m

The negative sign means the displacement is opposite the chosen positive direction. Its magnitude is 0.30 m.

Question 3

A planning estimate uses a displacement of

+0.60\,\mathrm{m}

3.0\,\mathrm{s}

. What average velocity does the model predict?

$+0.20\,\mathrm{m/s}$
$-0.20\,\mathrm{m/s}$
$+5.0\,\mathrm{m/s}$
$+0.20\,\mathrm{s/m}$

Show answer and explanation

+0.20\,\mathrm{m/s}

Divide displacement by elapsed time:

+0.60\,\mathrm{m}/3.0\,\mathrm{s}=+0.20\,\mathrm{m/s}

. The positive sign gives the chosen direction, and the units are metres per second.

Key terms

System: The object or group of objects selected for study.
Reference frame: The viewpoint and reference point used to describe motion.
Scalar: A quantity with size but no direction.
Vector: A quantity with both size and direction.
Independent variable: The factor deliberately changed or compared in an inquiry.
Dependent variable: The outcome measured in response to the changed factor.
Controlled variable: A factor kept consistent to make a comparison fair.
Average velocity: Displacement divided by elapsed time, including direction.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation B2.6. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

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