Speed vs velocity vs acceleration: read the graph correctly

The same downward-sloping line can describe different motion depending on the vertical axis. Before calculating anything, write down whether the graph shows position, velocity or acceleration.

Separate distance from displacement

Distance counts the length of the route. Displacement compares final position with starting position, including direction. Average speed is total distance divided by elapsed time; average velocity is displacement divided by elapsed time.

For an original example, walk 12 m east and then 12 m west in 8 s. Distance is 24 m, displacement is zero, average speed is 3 m/s and average velocity is zero. Returning to the start does not mean you were stationary throughout. OpenStax introduces displacement and average velocity here.

What each graph tells you

Graph	Height at a time	Slope	Area over a time interval
Position–time	Position	Velocity	Not distance or displacement
Velocity–time	Velocity	Acceleration	Displacement, using signed area
Acceleration–time	Acceleration	Rate of change of acceleration	Change in velocity

On a velocity–time graph, add the magnitudes of areas above and below zero to find distance. Adding the signed areas instead gives displacement. On a speed–time graph, the area directly gives distance.

For a curved position–time graph, use the tangent’s slope for instantaneous velocity and a secant’s slope for average velocity over an interval. The distinction between an instant and an interval is developed in OpenStax’s velocity and speed section.

Worked graph: slowing down, then speeding up

In this original example, velocity falls steadily from +2 m/s at 0 s to −2 m/s at 4 s. The object moves along a straight line with constant acceleration.

Acceleration: (−2 − 2) / 4 = −1 m/s², throughout the interval.

First two seconds: velocity is positive while acceleration is negative. Speed falls from 2 m/s to zero.

Next two seconds: velocity and acceleration are both negative. Speed rises from zero to 2 m/s, now in the opposite direction.

Each triangular area has magnitude ½ × 2 s × 2 m/s = 2 m. Displacement is +2 − 2 = 0 m; distance is 2 + 2 = 4 m. Over four seconds, average velocity is zero and average speed is 1 m/s.

The object is momentarily at rest at 2 s, but its acceleration is not zero. OpenStax explains acceleration and the role of signs.

Four traps to check before choosing an answer

“Negative acceleration means slowing down.” Compare it with velocity. In one dimension, equal signs mean increasing speed; opposite signs mean decreasing speed, away from the instant velocity is zero.

“Zero velocity means zero acceleration.” A turning point can have zero velocity and nonzero acceleration, as the example shows.

“A flat line means stationary.” A flat position graph means constant position. A flat velocity graph may mean steady motion at a nonzero speed.

“Average speed is always the mean of starting and finishing speeds.” Not generally. In the example, that would give 2 m/s, but distance divided by time gives 1 m/s.

Try explaining these differences without looking back at the table. If you can calculate the numbers but still confuse slope with height, record that distinction in your error log.