speed-time graph for the skater.","difficulty":2,"difficultyBand":"hard","totalMarks":6,"sourceTitle":null,"calculatorUse":"calc","parts":[{"id":"521d01de-16f7-4edf-a89a-0add9cb94eca","label":"a","content":"Work out the maximum speed of the speed skater during the race.","markscheme":"- Total area = 500 m M1\n- Let $v$ be max speed. Area = $\\frac{8v}{2} + (42.5 - 8)v = 500$ M1\n- $4v + 34.5v = 500 \\Rightarrow 38.5v = 500$ M1\n- $v = \\frac{500}{38.5} = 13.0 \\text{ ms}^{-1} \\text{ (3sf)}$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Equating total area under the graph to the total distance of 500m.","code":"M"},{"id":"p2","marks":1,"description":"Setting up a correct equation for the area using a variable for maximum speed.","code":"M"},{"id":"p3","marks":1,"description":"Simplifying the equation to solve for the maximum speed.","code":"M"},{"id":"p4","marks":1,"description":"Finding the correct maximum speed to 3 significant figures.","code":"A"}],"finalAnswers":["13.0","13.0 ms^-1"],"generatedAt":"2026-05-06T14:07:24.290Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"area_under_graph","label":"Area under the graph","steps":[{"type":"text","order":0,"title":"Use the area","content":"The area under a speed–time graph represents distance travelled. The race distance is 500 m, so the total area under the graph must be 500 m. This earns the first M1 mark.","highlights":[{"text":"race of 500 m","location":"specification"}]},{"type":"text","order":1,"title":"Split the graph","content":"Let the maximum speed be $v\\text{ m s}^{-1}$. The accelerating section is a triangle with base $8\\text{ s}$ and height $v$. The constant-speed section is a rectangle lasting $42.5-8=34.5\\text{ s}$.","highlights":[{"text":"accelerates at a constant rate for the first 8 seconds","location":"specification"},{"text":"maintains a constant speed for the rest of the race","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=triangle}{\\color{@sky}{\\dfrac{8v}{2}}}+\\htmlData{anchor=rectangle}{\\color{@sky}{(42.5-8)v}}=500$"},{"text":"Simplify the two area expressions."},{"latex":"$$\\htmlData{anchor=simplified}{\\color{@orange}{4v+34.5v}}=500$"}],"highlights":[{"color":"sky","anchor":"triangle"},{"color":"sky","anchor":"rectangle"},{"color":"orange","anchor":"simplified"}]},"order":2,"title":"Form the equation","description":"Add the triangle and rectangle areas, then set their total equal to the race distance. Writing this complete area equation earns the second M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=collected}{\\color{@sky}{38.5v=500}}$"},{"latex":"$$\\htmlData{anchor=quotient}{\\color{@amber}{v=\\frac{500}{38.5}}}$"},{"latex":"$$\\boxed{\\htmlData{anchor=answer}{\\color{@green}{v=13.0\\ \\mathrm{m\\ s^{-1}}\\ (3\\ \\mathrm{s.f.})}}}$"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"collected"},{"color":"green","style":"text-color-with-background","anchor":"answer"}]},"order":3,"title":"Solve for speed","description":"Collect the like terms, divide by 38.5, and give the maximum speed to 3 significant figures. Reaching 38.5v = 500 earns the third M1 mark; the boxed result earns the A1 mark."}]}],"generatedAt":"2026-07-19T18:26:47.532Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"706cf45c-d7c9-4cd2-9b49-3f91c922eda9","label":"b","content":"Calculate the distance covered by the speed skater in the first 8 seconds of the race.","markscheme":"- Area of triangle = $\\frac{1}{2} \\times \\text{base} \\times \\text{height}$ M1\n- $\\frac{8 \\times 12.987...}{2} = 51.9 \\text{ m (3sf)}$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Applying the formula for the area of a triangle using the previously calculated speed.","code":"M"},{"id":"p2","marks":1,"description":"Obtainin

Velocity Time Graphs

Question 1

Velocity Time Graphs Questions

Velocity Time Graphs

Question 1

Velocity Time Graphs Questions