fe56-ef6c-477f-b80d-c7b4ba5c241f","revisionId":"83a8dfe2-3930-4bd2-a982-b9d850f84fb7","questionNumber":null,"questionType":"LA","specification":"In a reaction-time experiment, a student holds a ruler vertically. A classmate places their open fingers level with the zero mark of the ruler, ready to catch it. Without warning, the student drops the ruler, and the classmate catches it as quickly as possible. The distance \$d\$ that the ruler falls before being caught is measured.","difficulty":7,"difficultyBand":"medium","totalMarks":8,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"23ddcd9d-0808-4b69-ab90-552ac252a8d0","label":"a","content":"Using equations of motion, derive the expression for the reaction time \$t\$ of the classmate in terms of the distance \$d\$ and the acceleration due to gravity \$g\$. Assume air resistance is negligible.","markscheme":"- Identifies $s = ut + \\frac{1}{2}at^2$ with $u = 0$, $s = d$, and $a = g$ M1\n- Simplifies to $d = \\frac{1}{2}gt^2$ A1\n- Rearranges to make $t$ the subject, yielding $t = \\sqrt{\\frac{2d}{g}}$ A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"derive_reaction_time","label":"Derive the reaction time","steps":[{"type":"text","order":1,"title":"Choose the motion equation","content":"Take downward as positive. The ruler starts from rest, so $s=d$, $u=0$, and $a=g$. The time for which the ruler is falling is the classmate's reaction time, so this fall time is $t$. Identifying these values in $s=ut+\\frac{1}{2}at^2$ earns the M1 mark.","highlights":[{"text":"Using equations of motion","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=motion-equation}{s = ut + \\frac{1}{2}at^2}"},{"latex":"\\htmlData{anchor=substituted-equation}{d = 0\\cdot t + \\frac{1}{2}gt^2}"},{"latex":"\\htmlData{anchor=simplified-equation}{d = \\frac{1}{2}gt^2}"}],"connections":[{"to":"substituted-equation","from":"motion-equation","color":"sky","label":"substitute"},{"to":"simplified-equation","from":"substituted-equation","color":"green","label":"zero term vanishes"}]},"order":2,"title":"Substitute the values","description":"Substitute the identified values. The zero term vanishes, giving d = 1/2 gt^2. This simplification earns A1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=rearranged-start}{\\frac{1}{2}gt^2 = d}"},{"latex":"\\htmlData{anchor=squared-time}{t^2 = \\frac{2d}{g}}"},{"latex":"\\htmlData{anchor=reaction-time}{t = \\sqrt{\\frac{2d}{g}}}"}],"connections":[{"to":"squared-time","from":"rearranged-start","color":"amber","label":"multiply both sides by 2/g"},{"to":"reaction-time","from":"squared-time","color":"green","label":"take the positive square root"}]},"order":3,"title":"Make t the subject","description":"Multiply both sides by 2/g to isolate t^2, then take the positive square root because time cannot be negative. This earns the final A1 mark."}]}],"generatedAt":"2026-07-22T11:28:30.368Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]},{"id":"c65da7b9-af2f-4fcf-919d-24dd80029bcd","label":"b","content":"In one trial, the ruler falls a distance of \$19.6\\text{ cm}\$ before it is caught. Calculate the classmate's reaction time, using \$g = 9.80\\text{ m/s}^2\$.","markscheme":"- Converts distance to meters: $d = 19.6\\text{ cm} = 0.196\\text{ m}$ B1\n- Substitutes $d = 0.196$ and $g = 9.80$ into their formula: $t = \\sqrt{\\frac{2 \\times 0.196}{9.80}}$ M1\n- Obtains $t = 0.20\\text{ s}$ A1","marks":3,"order":1,"markingRubric":null,"explanation":{"methods":[{"id":"suvat_rearrangement","label":"Rearrange the motion equation","steps":[{"type":"text","order":1,"title":"Choose the motion model","content":"The ruler starts from rest, so $u=0$. While it falls, its acceleration is $g$, and its displacement is $d$. Therefore use the constant-acceleration equation\n\n$$d=ut+\\frac12gt^2$$\n\nWith $u=0$, this becomes $d=\\frac12gt^2$.","highlights":[{"text"

Motion

Question 24

Motion Questions

Motion

Question 24

Motion Questions