Measure motion and compare position–time graphs

Learning goal: Describe motion using position, elapsed time, speed and direction. Build and interpret position–time graphs from evidence, keeping the graph's vertical coordinate distinct from total distance traveled.

Position describes where an object is relative to a reference. For a straight classroom route, choose a starting marker as zero and define increasing positions as east of that marker. State the unit, such as meters. Another observer may choose a different zero, so compare reference systems before deciding that two descriptions contradict each other.

Motion is a change in position over time relative to the chosen reference. Record the time at each observation and the object's corresponding position. A table pairs these values; a graph places time on the horizontal axis and position on the vertical axis. The line on the page represents those paired measurements, not the physical shape of the route on the floor.

The diagram compares three invented records over four seconds. Walker A starts at zero meters and reaches two, four, six and eight meters at seconds one, two, three and four. Walker B starts at zero and reaches one, two, three and four meters at those times. Object C stays at three meters throughout. Each record uses the same time and position scales.

A changes position by two meters in each one-second interval. B changes position by one meter in the same interval. A is moving faster along the route, represented by the steeper rising line. C's horizontal line indicates no position change, even though it is above zero on the graph. A high location on a graph does not by itself mean high speed.

For motion along this route without reversing, distance traveled divided by elapsed time gives average speed. A travels eight meters in four seconds, or two meters per second. B travels four meters in four seconds, or one meter per second. Describe their directions as eastward under the chosen route definition. Speed alone cannot distinguish two walkers moving equally fast in opposite directions.

The constant spacing of positions in these invented records models constant speed. Actual hand-recorded observations may vary because of changing pace or timing uncertainty. Connecting measured points can help display a pattern, but it does not prove the object moved at exactly one speed between observations. State whether a graph is an idealized model or a record of real measurements.

Position and total distance traveled are different quantities. A student who walks three meters east from zero and then three meters west returns to position zero but has traveled six meters. If that trip takes six seconds, the average speed for the whole trip is one meter per second. Dividing final position zero by six would incorrectly give zero speed despite the walking. This example clarifies the measurement; detailed reversing-motion graphs are left for later study.

Speed can also be measured and graphed as a function of time. In the invented records, A's speed is two meters per second throughout the four seconds, B's is one meter per second and C's is zero. The diagram's second panel graphs these speeds against time: each record is a horizontal line, at two, one and zero meters per second. On a speed–time graph a horizontal line means the speed is not changing; it means the object is at rest only when the line is at zero. On a position–time graph a horizontal line means the object is not moving. Always read the vertical-axis label before interpreting a line.

Use the same graph scales when comparing line steepness. A graph stretched vertically or squeezed horizontally can make the very same data look steeper. Compare coordinates and axis units before claiming one object is faster. Two separate pages with different scales cannot be compared reliably by the visual angle of their lines alone.

Direction also requires a reference. “Toward the door” works if the door's location is clear; “east” works if the route is oriented and labeled accordingly. A moving observer can give a different motion description from a stationary observer. Keep this investigation anchored to fixed floor markers so that the position record remains interpretable.

The purpose is to reason from measured changes over shared time intervals. You do not need to memorize a slope formula or calculate acceleration. Explain which object covers more distance in an equal time and point to specific measurements that support the claim. A useful graph lets another reader reconstruct your comparison.

Worked comparison: At two seconds, A is at four meters and B at two meters. Both started at zero and moved east without reversing. A has covered twice the distance in the same time. C remains at three meters; being ahead of B at that instant does not make C faster.

Worked elapsed time: A separate object travels six meters between the clock readings five seconds and eight seconds. The elapsed time is three seconds, so average speed is two meters per second. Dividing by the final clock reading eight would use the wrong interval.

Actual measurement sequence: With adult support, mark a clear straight route at measured intervals. Use walking speeds or a controlled toy vehicle, keep the area free of obstacles and assign observer roles. A video with a visible scale and timestamps may help. Record at least five time–position pairs for two trials, using the same reference and units. Do not replace observations with the fictional data.

Independent performance: Create a table and shared-axis graph, describe each trial's direction and compare relative speeds using equal-time intervals. Compute one average speed from a measured distance and its matching elapsed time. Identify uncertainty and repeat a trial to investigate it. Finally explain why a horizontal position line represents rest and why returning to the starting position does not imply zero distance traveled.