e velocity of a car for the first 10 seconds after it starts moving. The speeds at 2-second intervals are $0\\text{ m/s}$, $6.4\\text{ m/s}$, $10.2\\text{ m/s}$, $12.8\\text{ m/s}$, $14.6\\text{ m/s}$, and $15.6\\text{ m/s}$.\n\n![A speed-time graph for a car.](https://assets.mathsgenie.co.uk/questions/f5c857e3-64dd-4f74-b155-999456a3ee0c.png)","difficulty":3,"difficultyBand":"medium","totalMarks":4,"sourceTitle":null,"calculatorUse":"calc","parts":[{"id":"177bcda8-7224-4acb-a077-a8192ca0ddcb","label":"a","content":"Use 5 strips of equal width to find an estimate for the distance travelled in 10 seconds.","markscheme":"- Width $= 2$s. Heights at $t=0, 2, 4, 6, 8, 10$ are $0, 6.4, 10.2, 12.8, 14.6, 15.6$ M1\n- Area $\\approx 2 \\times [\\frac{0+6.4}{2} + \\frac{6.4+10.2}{2} + \\frac{10.2+12.8}{2} + \\frac{12.8+14.6}{2} + \\frac{14.6+15.6}{2}]$ M1\n- Area $\\approx 6.4 + 16.6 + 23.0 + 27.4 + 30.2 = 103.6$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correct identification of strip width (2) and ordinates.","code":"M"},{"id":"p2","marks":1,"description":"Correct application of the trapezium rule.","code":"M"},{"id":"p3","marks":1,"description":"Obtain final estimate of 103.6.","code":"A"}],"finalAnswers":["103.6"],"generatedAt":"2026-05-06T14:07:23.674Z","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 total time is $10$ seconds and there are $5$ equal strips, so each strip has width\n$$\n\\frac{10}{5}=2\\text{ s}.\n$$\nThe strip boundaries are therefore at $t=0,2,4,6,8,10$, with heights $0,6.4,10.2,12.8,14.6,15.6\\text{ m/s}$. Identifying this width and these heights earns the first **M1** mark.","highlights":[{"text":"Use 5 strips of equal width","location":"specification"}]},{"type":"graph","order":1,"title":"Join the strip tops","viewport":{"top":17.2,"left":-0.8,"right":10.9,"bottom":-1},"axisLabels":{"x":"Time (s)","y":"Speed (m/s)"},"description":"The indigo curve is the original speed–time graph. The blue straight chords form five trapezia, so the shaded area is an estimate of the area under the curve. The dashed lines show the equal strip boundaries.","expressions":[{"id":"expr-0","color":"indigo","latex":"y=4.268333333x-0.677083333x^2+0.082291667x^3-0.005729167x^4+0.00015625x^5\\left\\{0\\le x\\le10\\right\\}","lineStyle":"solid"},{"id":"expr-1","color":"indigo","label":"original curve","latex":"\\left(1,3.66796875\\right)","hidden":true,"labelOrientation":"above"},{"id":"expr-2","color":"sky","latex":"0\\le y\\le\\left\\{0\\le x\\le2:3.2x,2

Velocity Time Graphs

Question 4

Velocity Time Graphs Questions

Velocity Time Graphs

Question 4

Velocity Time Graphs Questions