<p>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.</p>
<p style="text-align: center">\[\text{speed}=\left|\frac{\text{change in position}}{\text{change in time}}\right|\] for a straight segment. For a curved segment, use the magnitude of the tangent gradient.</p>
<p>2.	Types of Distance-Time Graphs</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center"><p>Straight line</p></th><th style="text-align: center; --cell-justify: center"><p>Curve</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765953389369-dwj7zfvxa3k.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU5NTMzODkzNjktZHdqN3pmdnhhM2sucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MTQ1OTc1MiwiZXhwIjoxNzkxNDYwMDUyfQ.ujC3Czd2Fg85jwyN-d1N3Dqm5pxpiyXyhCir1d8V214"></p></td><td style="text-align: center; --cell-justify: center"><p><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765953413859-roownkv2v8p.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU5NTM0MTM4NTktcm9vd25rdjJ2OHAucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MTQ1OTc1MiwiZXhwIjoxNzkxNDYwMDUyfQ.Akqz6CLBv4HKIxBqSAEk6CwspaBR_vEhEzhILEoIVes"></p></td></tr><tr><td style="text-align: center; --cell-justify: center">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.</td><td style="text-align: center; --cell-justify: center">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.</td></tr></tbody></table></div></div>
<p>3.	\(\text{Average \ Speed =}\hspace{0.5em}\frac{\text{Total \ Distance \ Travelled}}{\text{Total \ Time \ Taken}}\).	</p>
<p>4.	Increasing and decreasing speed</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765953473692-ixu234n1rnh.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU5NTM0NzM2OTItaXh1MjM0bjFybmgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MTQ1OTc1MiwiZXhwIjoxNzkxNDYwMDUyfQ.5XfKGqwE0njzuO6tnHb8XZTsmWGQ8xRM8rxWI73FraQ" style="max-width: min(600px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

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.

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

Distance-Time Graphs

Distance-Time Graphs

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