1. For a cumulative-distance graph, the gradient is speed. A graph of distance from a fixed starting point can decrease; in straight-line motion without crossing that point, speed is the magnitude of its gradient. \[\text{speed}=\left|\frac{\text{change in position}}{\text{change in time}}\right|\] for a straight segment. For a curved segment, use the magnitude of the tangent gradient. 2. Types of Distance-Time Graphs Straight line Curve Each straight segment represents a constant speed on that segment. A horizontal segment is rest. Different segments can have different speeds. A descending distance-from-origin segment indicates motion back towards the origin; its speed is the absolute gradient.A changing tangent gradient indicates changing speed. Compare gradient magnitudes, including on descending parts. A steeper downward slope means a greater speed towards the origin. 3. \(\text{Average \ Speed =}\hspace{0.5em}\frac{\text{Total \ Distance \ Travelled}}{\text{Total \ Time \ Taken}}\). 4. Increasing and decreasing speed

Distance-Time Graphs

Secondary 3

1. For a cumulative-distance graph, the gradient is speed. A graph of distance from a fixed starting point can decrease; in straight-line motion without crossing that point, speed is the magnitude of its gradient.

\[\text{speed}=\left|\frac{\text{change in position}}{\text{change in time}}\right|\] for a straight segment. For a curved segment, use the magnitude of the tangent gradient.

2. Types of Distance-Time Graphs

Straight line	Curve

Each straight segment represents a constant speed on that segment. A horizontal segment is rest. Different segments can have different speeds. A descending distance-from-origin segment indicates motion back towards the origin; its speed is the absolute gradient.	A changing tangent gradient indicates changing speed. Compare gradient magnitudes, including on descending parts. A steeper downward slope means a greater speed towards the origin.

3. \(\text{Average \ Speed =}\hspace{0.5em}\frac{\text{Total \ Distance \ Travelled}}{\text{Total \ Time \ Taken}}\).

4. Increasing and decreasing speed

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