Graphical Representation of Motion

On a distance–time graph, the y-axis represents distance and the x-axis represents time. A horizontal (flat) line means the distance value is not changing as time passes.

If distance does not change over time, the object has not moved from its position. This means the object is stationary (at rest).

The gradient of a flat line is $\frac{\Delta d}{\Delta t}=\frac{0}{10}=0$ m/s. A speed of zero confirms the object is not moving.

A flat horizontal line on a distance–time graph always means the object is stationary.

We need to match a flat horizontal line on a distance–time graph to the correct motion description.

Constant speed on a distance–time graph is shown by a straight diagonal line (not flat), because distance is increasing steadily. So this option is incorrect.

Acceleration on a distance–time graph is shown by a curve that gets steeper, because more distance is covered each second. A flat line cannot represent acceleration.

Deceleration is shown by a curve that gets shallower (still going upward but less steeply). A flat line does not match this either.

The only remaining option is stationary, which is correct — a flat line means zero change in distance, so the object is not moving.

The speed of an object equals the gradient of the distance–time graph: $\text{Speed}=\frac{\Delta d}{\Delta t}$

Using the two points $(0\text{ s},5\text{ m})$ and $(10\text{ s},45\text{ m})$: $\Delta d=45-5=40\text{ m}$

$\Delta t=10-0=10\text{ s}$

$\text{Speed}=\frac{40}{10}=4\text{ m/s}$

The object is travelling at a constant speed of 4 m/s.

Speed = gradient = $\frac{\Delta d}{\Delta t}$. We have $\Delta d=45-5=40$ m and $\Delta t=10-0=10$ s, so speed $=\frac{40}{10}=4$ m/s.

40 m/s is just the change in distance ($\Delta d$), not the speed. You must divide by the change in time, not just read off $\Delta d$.

5 m/s would come from incorrectly dividing $\frac{45}{10}=4.5\approx 5$, or from using the wrong starting point. This ignores the fact that the graph starts at $d=5$ m, not 0.

9 m/s could result from incorrectly adding $\frac{45+5}{10}=\frac{50}{10}=5$, or another arithmetic error. This is not the correct gradient calculation.

The correct speed is 4 m/s, calculated as $\frac{\Delta d}{\Delta t}=\frac{40}{10}=4$ m/s.