// Numbas version: finer_feedback_settings {"name": "SUVAT equations question 4", "extensions": [], "custom_part_types": [], "resources": [["question-resources/man_image.png", "/srv/numbas/media/question-resources/man_image.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["t", "km"], "name": "SUVAT equations question 4", "tags": [], "advice": "

a) It is important to always convert your measurements to base SI units before using the SUVAT equations. For velocity, the SI units are $\\mathrm{ms^{-1}}$. We have $\\mathrm{km \\ h^{-1}}$, where $1\\mathrm{km} = 1000\\mathrm{m}$ and $1\\mathrm{h} = 60 \\times 60 \\mathrm{s} = 3600\\mathrm{s}$.

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Therefore

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 \\begin{align} \\var{km} \\mathrm{km \\ h^{-1}} & = \\var{km} \\times 1000 \\div 3600 \\mathrm{ms^{-1}},\\\\                                                                 & = \\var[fractionNumbers]{km*1000/3600}\\mathrm{ms^{-1}}. \\end{align}  

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b)  As the pedestrian starts from rest $u=0$. Then we have $v=\\var[fractionNumbers]{km*1000/3600}$, $t=\\var{t}$, $a=?$ and $s=?$. We want $a$ so we can use $v=u+at$ rearranged for $a$, remembering to use our $v$ in SI units from part a).

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\\begin{align} a &= \\frac{v-u}{t}, \\\\
                       &= \\frac{\\var[fractionNumbers]{km*1000/3600} - 0}{\\var{t}}, \\\\
                       &= \\var[fractionNumbers]{(km*1000/3600)/t} \\mathrm{ms^{-2}}. \\end{align}

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The acceleration of the pedestrian is $\\var[fractionNumbers]{(km*1000/3600)/t} \\mathrm{ms^{-2}}.$

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c) We want the distance, $s$. So we use $s = \\left(\\frac{u+v}{2}\\right)t$.

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\\begin{align} s & =  \\left(\\frac{u+v}{2}\\right)t, \\\\
                       & =  \\left(\\frac{0+\\var[fractionNumbers]{km*1000/3600}}{2}\\right)\\times \\var{t}, \\\\
                       & = \\var[fractionNumbers]{(km*1000/3600)*0.5*t} \\mathrm{m}.\\end{align}

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The distance between the crossing and the shop is $\\var[fractionNumbers]{(km*1000/3600)*0.5*t}\\mathrm{m}.$

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Convert $\\var{km} \\mathrm{km \\ h^{-1}}$ into SI units $\\mathrm{ms^{-1}}$ (enter your answer as a fraction).

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What is the pedestrain's accelerationin $\\mathrm{ms^{-2}}$?

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Find the distance in $\\mathrm{m}$ from the crossing to the shop.

", "allowFractions": true, "variableReplacements": [], "maxValue": "(km*1000/3600)*0.5*t", "minValue": "(km*1000/3600)*0.5*t", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "

A pedestrian waits at a crossing until the road is clear. He crosses the road with constant acceleration, starting from rest and $\\var{t}$ seconds later he passes a shop and is travelling at $\\var{km} \\mathrm{km \\ h^{-1}}.$ 

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time he passes the shop

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pedestrains speed in km. students convert to metres.

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