\\,000 = 0.5 \\times 120 \\times v^2$ (or rearrangement: $v^2 = \\frac{2 \\times 216\\,000}{120}$) M1\n- Correct calculation of $v^2$ as $3600$ (or $v = \\sqrt{3600}$) M1\n- Correct final speed of $60\\text{ m/s}$ (accept $60$) A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"rearrange_ke","label":"Rearrange the kinetic energy equation","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"216\\,000 = 0.5 \\times 120 \\times v^2"},{"latex":"216\\,000 = 60v^2"}]},"order":1,"title":"Substitute the values","description":"Replace kinetic energy and mass with the given values, leaving v as the unknown. This correct substitution earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"216\\,000 = \\htmlData{anchor=sixty}{60}v^2"},{"latex":"v^2 = \\frac{216\\,000}{\\htmlData{anchor=divisor}{60}}"},{"latex":"\\htmlData{anchor=v-squared}{v^2}=3600"}],"highlights":[{"color":"green","style":"box","anchor":"v-squared"}],"connections":[{"to":"divisor","from":"sixty","color":"orange","label":"divide by 60"}]},"order":2,"title":"Find speed squared","description":"Divide both sides by 60 to leave v squared on its own. Getting this value earns the second M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"v^2 = \\htmlData{anchor=square-value}{3600}"},{"latex":"v = \\sqrt{\\htmlData{anchor=root-value}{3600}}"},{"latex":"\\boxed{v=60\\text{ m/s}}"}],"connections":[{"to":"root-value","from":"square-value","color":"green","label":"square root"}]},"order":3,"title":"Take the square root","description":"The equation gives v squared, not v, so take the positive square root. Speed cannot be negative here. This final answer earns A1."}]}],"generatedAt":"2026-07-22T09:18:03.264Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"14ab4668-8ecf-42b3-a71e-03b74831901b","revisionId":"3bcae9e6-d95c-46a9-b8c8-d91190bbba98","questionNumber":null,"questionType":"LA","specification":"","difficulty":4,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"11b3d0de-e42d-4ddb-b8f6-a6ea16761d50","label":null,"content":"As seawater flows through a tidal turbine generator, the kinetic energy of a $18.0\\text{ kg}$ mass of moving water is $576\\text{ J}$.\n\nCalculate the speed of this water as it passes through the turbine.\n\nUse the equation:\n$$\\text{kinetic energy} = 0.5 \\times \\text{mass} \\times \\text{speed}^2$$\n\nShow your working.","markscheme":"- Substitutes the given values into the kinetic energy equation, $576 = 0.5 \\times 18.0 \\times v^2$, or rearranges to $v^2 = \\frac{2 \\times 576}{18.0}$ M1\n- Obtains $v^2 = 64$ or $v = \\sqrt{64}$ A1\n- Finds the speed to be $8.0\\text{ m/s}$ (accept $8$) A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"rearrange_ke","label":"Rearrange the kinetic-energy equation","steps":[{"type":"text","order":0,"title":"Choose the equation","content":"The question gives kinetic energy, mass and asks for speed, so use the stated equation. Let $v$ represent the speed in $\text{m/s}$.\n\nThe mass is already in $\text{kg}$ and the energy is already in $\text{J}$, so no unit conversion is needed.","highlights":[{"text":"kinetic energy of a $18.0\\text{ kg}$ mass of moving water is $576\\text{ J}$","location":"specification"},{"text":"Calculate the speed of this water","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"E_k=0.5\\times m\\times v^2"},{"latex":"576=0.5\\times18.0\\times\\htmlData{anchor=speed-squared}{v^2}"}],"highlights":[{"color":"green","style":"box","anchor":"speed-squared"}]},"order":1,"title":"Substitute the values","description":"Put the kinetic energy and mass into the equation, leaving the speed as the unknown. This substitution earns the first mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"v^2=\\frac{2\\times576}{18.0}"},{"latex":"v^2=\\htmlData{anchor=speed-s

Energy stores, work done and energy calculations

Question 2

Energy stores, work done and energy calculations Questions

Energy stores, work done and energy calculations

Question 2

Energy stores, work done and energy calculations Questions