{"type":"hyper_latex","block":{"nodes":[{"latex":"$$a=\\dfrac{\\Delta v}{\\Delta t}$"},{"latex":"$$a=\\dfrac{\\htmlData{anchor=speeds}{\\color{@sky}{5-11}}}{\\htmlData{anchor=times}{\\color{@orange}{10-6}}}$"},{"latex":"$$a=\\htmlData{anchor=fraction}{\\dfrac{\\htmlData{anchor=dv}{\\color{@sky}{-6}}}{\\htmlData{anchor=dt}{\\color{@orange}{4}}}}$"},{"latex":"$$\\htmlData{anchor=answer}{\\color{@green}{a\\approx -1.5\\,\\mathrm{m/s^2}}}$"}],"highlights":[{"color":"green","style":"text-color","anchor":"answer"}],"connections":[{"to":"dv","from":"speeds","color":"sky","label":"subtract speeds"},{"to":"dt","from":"times","color":"orange","label":"subtract times"},{"to":"answer","from":"fraction","color":"green","label":"divide"}]},"order":3,"title":"Calculate the gradient","description":"The selected tangent coordinates are approximate readings from the graph. Use gradient = change in speed divided by change in time. The negative sign shows that the speed is decreasing. This correct estimated gradient earns A1."}]}],"generatedAt":"2026-07-19T19:09:10.942Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"9eb4e81e-a3cf-4969-81f4-a1c0b919f970","label":"b","content":"Use 5 strips of equal width to find an estimate for the distance the toy car travels in the first 10 seconds.","markscheme":"- Width of each strip = 2s. Heights at $t=0, 2, 4, 6, 8, 10$ are $0, 5, 12, 15, 14, 10$ M1\n- Area $\\approx 2 \\times [\\frac{0+5}{2} + \\frac{5+12}{2} + \\frac{12+15}{2} + \\frac{15+14}{2} + \\frac{14+10}{2}]$ M1\n- Area $\\approx 2 \\times [2.5 + 8.5 + 13.5 + 14.5 + 12] = 102$ A1","marks":3,"order":1,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Identifies strip width of 2 and reads appropriate heights from the graph.","code":"M"},{"id":"p2","marks":1,"description":"Summing the area of the 5 strips correctly using the trapezium method.","code":"M"},{"id":"p3","marks":1,"description":"Correct distance estimate of approximately 102.","code":"A"}],"finalAnswers":["102"],"generatedAt":"2026-05-06T14:07:12.417Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"trapezium_rule","label":"Trapezium rule","steps":[{"type":"text","order":0,"title":"Find the strip width","content":"The first $10$ seconds are divided into $5$ equal strips, so each strip has width\n\n$$\\frac{10}{5}=2\\text{ s}.$$","highlights":[{"text":"Use 5 strips of equal width","location":"specification"},{"text":"in the first 10 seconds","location":"specification"}]},{"type":"graph","order":1,"title":"Read the six heights","viewport":{"top":16.5,"left":-1,"right":11,"bottom":-1},"axisLabels":{"x":"Time (seconds)","y":"Speed (m/s)"},"description":"Read the speed at each strip boundary: $0$, $5$, $12$, $15$, $14$ and $10$ m/s. Using the strip width $2$ s together with these six heights earns the first M1.","expressions":[{"id":"expr-0","color":"sky","latex":"y=\\left\\{0\\le x\\le2:1.25x^2,\\ 2

Velocity Time Graphs

Question 10

Velocity Time Graphs Questions

Velocity Time Graphs

Question 10

Velocity Time Graphs Questions