Measure speed and distinguish constant from changing motion

Learning goal: Measure how far an object travels during a measured time and use successive equal-time intervals to identify constant speed, speeding up and slowing down. Speed describes how fast position changes along a path. A useful calculation is distance traveled divided by elapsed time, but the number must be interpreted in its measurement context.

An object traveling six meters in three seconds has an average speed of two meters per second over that interval. This means its measured distance is equivalent to two meters for each second on average. It does not prove that it traveled exactly two meters during every individual second. The object might have sped up, slowed down or paused during the trip.

To investigate changing speed, record position repeatedly at equal time intervals along a straight path. A fictional cart A has positions zero, two, four and six meters at times zero, one, two and three seconds. It travels two meters during each successive second. Those observations support constant speed over the measured intervals, with finer changes between observations still unresolved.

A fictional cart B reaches positions zero, one, three and six meters at those same times. Its successive one-second distances are one, two and three meters. Increasing distance in equal time indicates speeding up. Cart C reaches zero, three, five and six meters; its successive distances are three, two and one meters, indicating slowing down. All three carts travel six meters in three seconds and share the same whole-trip average speed, despite different interval patterns.

The diagram places each time-stamped marker on one common distance scale. For A, equal marker spacing represents equal distance in equal time. For B, gaps grow. For C, gaps shrink. Read the timestamps before interpreting spacing: growing distances measured over growing amounts of time would not by themselves establish speeding up.

Distance traveled and final position are different ideas. A toy moves two meters away from its starting point and then two meters back in four seconds. Its total travel distance is four meters, so average speed is one meter per second. Its final position is the starting point. Dividing zero change in position by four seconds would not calculate the average speed along its out-and-back path.

Use compatible units. For a cart traveling 120 centimeters in two seconds, average speed is sixty centimeters per second. That is 0.6 meters per second because 120 centimeters equals 1.2 meters. Label the distance and elapsed time before calculating; a bare answer of sixty leaves the reader unable to tell what was measured.

Timing introduces uncertainty. Human start/stop reactions can have a large effect on a very short trip. Mark clear start and finish lines, measure the path, use the same trigger rule and repeat trials. A video showing the cart and a time reference can help identify when it crosses each mark. Do not call small differences meaningful without considering measurement precision and variation among trials.

Speed is only one aspect of motion. A ball traveling around a curve can maintain speed while changing direction; its motion still changes. In the companion force lesson, unbalanced forces explain changes in speed or direction: a greater force acting for the same time produces a greater change in motion, and the same force acting for the same time changes a more massive object's motion less. Together the two lessons cover 5.PS.1. This lesson measures the observed motion rather than inferring a force's strength from a single distance alone.

Worked interval analysis: For positions 0, 1, 3 and 6 meters, subtract neighboring positions: 1 − 0 = 1, 3 − 1 = 2 and 6 − 3 = 3 meters. Each difference belongs to one second. The growing differences support speeding up; the whole-trip calculation 6 ÷ 3 = 2 meters per second hides that pattern.

Worked measurement: A toy covers a measured 90-centimeter path in three seconds. Its average speed is thirty centimeters per second. A second toy covers sixty centimeters in the same time, averaging twenty centimeters per second. The first has the greater average speed because it covers more distance during equal elapsed time.

Guided investigation: Measure a clear, level path and record a safely moving toy or a person walking. An adult helps with timing or video. Retain distance units, timestamps and at least three repeated measurements. Avoid roads, stairs and racing. Calculate each trial's average speed and explain variation rather than replacing observations with the fictional cart data.

Independent performance: Design a method to distinguish steady from changing speed, collect positions at equal time intervals, calculate interval distances and communicate the pattern with a labeled display. Explain what the measurements can and cannot reveal between samples. Then critique a claim that equal trip averages prove identical motion throughout a trip.