lVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"0fcd8478-7060-4542-ba85-7369040e891c","label":"b","content":"Find the speed at which the stone hits the ground.","markscheme":"- Use $s = -2, u = 18, a = -9.8$. Use $v^2 = u^2 + 2as$ M1\n- $v^2 = 18^2 + 2(-9.8)(-2) = 324 + 39.2 = 363.2$ M1\n- $v = \\sqrt{363.2} \\approx 19 \\text{ ms}^{-1}$ (2sf) A1","marks":3,"order":1,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Uses $s=-2$ in a suvat equation.","code":"M"},{"id":"p2","marks":1,"description":"Calculates $v^2$.","code":"M"},{"id":"p3","marks":1,"description":"Obtains $19$.","code":"A"}],"finalAnswers":["19"],"generatedAt":"2026-05-12T02:14:06.558Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"suvat","label":"Use a SUVAT equation","steps":[{"type":"text","order":0,"title":"Set the signs","content":"Take upwards as positive. At the ground, the displacement from the starting point is $s=-2$, the initial velocity is $u=18$, and the acceleration is $a=-9.8$. **Examiner annotation: M1: use $s=-2$, $u=18$ and $a=-9.8$ in $v^2=u^2+2as$.**","highlights":[{"text":"Find the speed at which the stone hits the ground.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$v^2=18^2+2(-9.8)(-2)$"},{"latex":"$$v^2=324+39.2$"},{"latex":"$$v^2=363.2$"}]},"order":1,"title":"Calculate squared speed","description":"Calculate the squared speed. The correct value 363.2 earns the second M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=root_start}{v=\\sqrt{363.2}}$"},{"latex":"$$\\htmlData{anchor=final_speed}{\\boxed{\\color{@green}{v\\approx19\\ \\mathrm{m\\,s^{-1}}}}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"root_start"},{"color":"green","style":"text-color-with-background","anchor":"final_speed"}],"connections":[{"to":"final_speed","from":"root_start","color":"orange","label":"round to 2 s.f.","style":"solid"}]},"order":2,"title":"Take the positive root","description":"Because the question asks for speed, take the positive root. A1: v = square root of 363.2 is approximately 19 m s^-1 to 2 significant figures."}]}],"generatedAt":"2026-07-21T04:12:18.498Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"c62f045b-4538-463b-b58e-978f4ad46d9a","label":"c","content":"Find the time between the instant the stone is projected and when it hits the ground.","markscheme":"- Use $s = ut + \\frac{1}{2}at^2$: $-2 = 18t - 4.9t^2$ M1\n- $4.9t^2 - 18t - 2 = 0$ M1\n- Solve quadratic: $t = 3.8 \\text{ s}$ A1","marks":3,"order":2,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Sets up quadratic equation for $t$.","code":"M"},{"id":"p2","marks":1,"description":"Solves quadratic equation.","code":"M"},{"id":"p3","marks":1,"description":"Obtains $3.8$.","code":"A"}],"finalAnswers":["3.8"],"generatedAt":"2026-05-12T02:14:06.558Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"suvat_quadratic","label":"SUVAT then solve a quadratic","steps":[{"type":"text","order":0,"title":"Choose signs and displacement","content":"Take upwards as positive. The stone starts $2\\text{ m}$ above the ground, so its displacement when it reaches the ground is $s=-2$. Its initial velocity is $u=18$, and gravity gives $a=-9.8$.\n\nWe need the time $t$, so use the constant-acceleration equation $s=ut+\\frac12at^2$.","highlights":[{"text":"projected vertically upwards with a speed $18\\text{ms}^{-1}$ from a point 2 m above the ground","location":"specification"},{"text":"Find the time between the instant the stone is projected and when it hits the ground.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"s=ut+\\frac{1}{2}at^2"},{"latex":"-2=18t+\\htmlData{anchor=halfaccel}{\\color{@sky}{\\frac{1}{2}(-9.8)}}t^2"},{"latex":"-2=18t+\\htmlData{anchor=simplifiedterm}{\\color{@sky}{(-4.9t^2)}}"}],"highlights":[{"color":"sky","style":"

Constant Acceleration

Question 9

Constant Acceleration Questions

Constant Acceleration

Question 9

Constant Acceleration Questions