b","content":"Find the speed of the ball as it hits the ground.","markscheme":"- Use $v = u + at$: $v = 20 + (-9.8)(5)$ M1\n- $v = -29 \\text{ ms}^{-1}$ A1\n- Speed = $29 \\text{ ms}^{-1}$ A1","marks":3,"order":1,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Uses $v = u + at$ or $v^2 = u^2 + 2as$.","code":"M"},{"id":"p2","marks":1,"description":"Calculates velocity as $-29$.","code":"A"},{"id":"p3","marks":1,"description":"States speed as positive magnitude $29$.","code":"A"}],"finalAnswers":["29"],"generatedAt":"2026-05-12T02:14:06.558Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"constant_acceleration","label":"Use the velocity formula","steps":[{"type":"text","order":0,"title":"Choose a direction","content":"Take **upwards as positive**. The ball is projected upwards, so $u=20\\text{ m s}^{-1}$. Gravity acts downwards, so $a=-9.8\\text{ m s}^{-2}$. The time of flight is $t=5\\text{ s}$.","highlights":[{"text":"projected vertically upwards with a speed of $20 \\text{ m s}^{-1}$","location":"specification"},{"text":"hits the ground 5 s later","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$v=\\htmlData{anchor=formula}{\\color{@sky}{u+at}}$"},{"latex":"$$v=\\htmlData{anchor=substitution}{\\color{@sky}{20+(-9.8)(5)}}$"},{"latex":"$$v=-29\\text{ m s}^{-1}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"formula"},{"color":"sky","style":"text-color-with-background","anchor":"substitution"}],"connections":[{"to":"substitution","from":"formula","color":"sky","label":"substitute values","style":"solid"}]},"order":1,"title":"Substitute into the formula","description":"Use the constant-acceleration formula shown below. Correct substitution of the signed acceleration and time earns M1; obtaining the signed velocity earns the first A1."},{"type":"text","order":2,"title":"Convert to speed","content":"The negative sign shows that the ball is moving downwards. Speed is the magnitude of velocity, so\n\n$$\\text{speed}=|-29|=29\\text{ m s}^{-1}.$$ \n\nTaking the magnitude to give the speed earns the final A1."}]}],"generatedAt":"2026-07-20T16:25:14.742Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":48}},{"id":"c1ae3e25-438d-4fca-b661-0fd33cf901be","revisionId":"0f936f20-5ffe-44d0-b75b-1bde215f48b3","questionNumber":"3","questionType":"LA","specification":"A car passes point A with a speed of $20 \\text{ km/h}$. The car accelerates at a constant rate and 10 seconds later it passes point B with a speed of $70 \\text{ km/h}$.","difficulty":2,"difficultyBand":"medium","totalMarks":6,"sourceTitle":"Question Set 1: Constant Acceleration","calculatorUse":null,"parts":[{"id":"b052ba0f-2d1b-4789-8dc1-05dd634d8905","label":"a","content":"Find the acceleration of the car in $\\text{ms}^{-1}$.","markscheme":"- Convert speeds to m/s: $20 \\text{ km/h} = \\frac{50}{9} \\text{ m/s}$, $70 \\text{ km/h} = \\frac{175}{9} \\text{ m/s}$ M1\n- Use $v = u + at$: $\\frac{175}{9} = \\frac{50}{9} + 10a$ M1\n- $a = \\frac{25}{18} \\approx 1.39 \\text{ ms}^{-2}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Converts km/h to m/s correctly.","code":"M"},{"id":"p2","marks":1,"description":"Applies $v = u + at$ with converted units.","code":"M"},{"id":"p3","marks":1,"description":"Obtains $1.39$ (or $25/18$).","code":"A"}],"finalAnswers":["1.39"],"generatedAt":"2026-05-12T02:14:06.558Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"constant_acceleration","label":"Use constant acceleration","steps":[{"type":"text","order":0,"title":"Identify the quantities","content":"Take the direction from A to B as positive. Then the initial speed is $u=20\\text{ km/h}$, the final speed is $v=70\\text{ km/h}$, and the time is $t=10\\text{ s}$. Because the required acceleration uses seconds, first convert both

Constant Acceleration

Question 2

Constant Acceleration Questions

Constant Acceleration

Question 2

Constant Acceleration Questions