Average Speed, Velocity, and Distance-Time Graphs

Distance and average speed

Motion means an object changes position over time. To describe it, we measure two things: how far the object moved and how long it took.

Why divide? Speed tells you how much distance you cover in each unit of time. If you cover 10 meters every second, your speed is 10 meters per second, written 10 m/s.

Science uses SI units: distance in meters (m) or kilometers (km), time in seconds (s) or hours (h). So speed is in m/s or km/h. On a highway sign you'll see miles per hour (mph), but in science class we usually use m/s.

It's called average speed because real objects speed up and slow down. The formula tells you the constant speed that would cover the same distance in the same time.

Sometimes the time is not in seconds. Convert first so the units match. For example, 2 minutes 30 seconds is $2\times 60 + 30 = 150$ s.

Speed, velocity, distance, and displacement

Imagine two friends who both travel at 15 m/s. One goes north and the other goes south. They have the same speed, but they are not moving the same way. Velocity captures that difference.

In the same way, we have two ways to describe how far something went:

• Distance is the length of the whole path traveled. It is never negative and ignores direction.

• Displacement is the straight-line change in position from the start to the end, with a direction. It only compares where you began with where you ended.

Notice the pattern: average velocity uses displacement divided by time, so it needs a direction. If the object ends where it started, the displacement is 0 m and the average velocity is 0 m/s, even though the speed is not zero.

Back to the start: Aaliyah ran 400 m, so her distance is 400 m. She finished at her starting line, so her displacement is 0 m. Both statements are true because distance and displacement measure different things.

Distance-time graphs

A distance-time graph shows how far an object has traveled as time passes. Time goes on the horizontal axis (x) and distance on the vertical axis (y). Each point tells you "at this time, the object was this far away." To collect the data, mark distances with a metric ruler or measuring tape and use a stopwatch or timer to record the time at each mark. Then record the pairs in a data table and plot each pair as a point, in SI units (meters and seconds).

Use the widget below. Slide the speed and watch the graph. The steeper the line, the faster the motion.

The big idea: the slope of a distance-time graph is the speed. Slope is rise over run, which is distance divided by time.

Tables of data work the same way. If the distance increases by the same amount in each equal time interval, the speed is constant and the graph is a straight line.

Summary

• Average speed $= \dfrac{\text{total distance}}{\text{total time}}$, in units such as m/s or km/h. Convert time to seconds when needed.

• Distance is the length of the path traveled. Displacement is the straight-line change in position, with a direction.

• Speed has only a size. Velocity has a size and a direction, and uses displacement. If you end where you started, displacement and average velocity are 0.

• On a distance-time graph, the slope is the speed. A flat line means at rest, and a steeper line means faster.

• Average speed for a whole trip is total distance over total time, not the average of the speeds in each part.

• Back to the track: Aaliyah's distance was 400 m, but her displacement was 0 m.