Reading the shape of the line

Without calculating anything, a great deal can be said about a motion just by looking at the shape of a displacement–time graph.

t (s)	0	4	6	8
s (m)	0	10	10	0

The graph above has three stages. Let us read each one.

0 – 4 s · the line rises

The displacement increases: the object is moving away from its starting point. The line is straight, so the velocity is uniform.

4 – 6 s · the line is flat

The displacement does not change, so the object has not moved — it is at rest. The gradient is zero, so the velocity is zero.

6 – 8 s · the line falls

The displacement decreases. The object is moving in the opposite direction, back towards where it started. The gradient is negative, so the velocity is negative.

Shape and meaning

Shape of the line	Gradient	The motion
Rising, steep	Large positive	Moving away quickly
Rising, shallow	Small positive	Moving away slowly
Flat	Zero	At rest
Falling	Negative	Coming back

Look at the slope, not the height

On a displacement–time graph, a line being high up does not mean the object is fast — it means the object is far from where it started. Speed is told by the slope.