// Numbas version: finer_feedback_settings {"name": "Simon's copy of Constant deceleration", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "parts": [{"showFeedbackIcon": true, "showPrecisionHint": false, "variableReplacements": [], "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "minValue": "(u^2+2*a*s)^(1/2)", "mustBeReducedPC": 0, "allowFractions": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "customMarkingAlgorithm": "", "marks": 1, "notationStyles": ["plain", "en", "si-en"], "precision": "3", "showCorrectAnswer": true, "type": "numberentry", "prompt": "

Find the speed of the caravan in $\\mathrm{ms}^{-1}$ after it has travelled $\\var{s} \\, \\mathrm{m}$. 

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How many seconds does the caravan take to travel $\\var{s} \\, \\mathrm{m}$?

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Find the tension in Newtons in the rope which pulls the caravan.

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If the caravan does experience a resistance to motion of magnitude $\\var{resistance} \\, \\mathrm{N}$, what would the tension in the rope be, in Newtons?

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A caravan pulled along by a car. Question uses SUVAT equations and $F=ma$.

"}, "name": "Simon's copy of Constant deceleration", "advice": "

a)

\n

We are told that the caravan is decelerating at a rate of $a= \\var{a} \\ \\mathrm{ms^{-2}}$. We know $u=\\var{u}$ and $s=\\var{s}$ and we want $v$, therefore we can use the equation $v^2=u^2+2as$.

\n

\\begin{align}
v^2 & = u^2 + 2as \\\\
& = \\var{u}^2 + \\left( 2 \\times \\var{a} \\times \\var{s} \\right) \\\\
& = \\var{u^2 + 2*a*s}
\\end{align}

\n

Therefore $v = \\sqrt{\\var{u^2 + 2*a*s}} = \\var{v}$. So the speed is $\\var{v} \\ \\mathrm{ms^{-1}}$.

\n

b)

\n

Having worked out the speed $v$ of the caravan after it has travelled $\\var{s} \\, \\mathrm{m}$, we can use the formula $v = u + at$ to find the time taken.

\n

\\begin{align}
v &= u + at \\\\
t &= \\frac{v-u}{a} \\\\
&= \\simplify[!basic]{({v}-{u})/{a}} \\\\
&= \\var{precround((v-u)/a,3)}
\\end{align}

\n

The caravan takes $\\var{precround((v-u)/a,3)} \\, \\mathrm{s}$ to travel $\\var{s} \\, \\mathrm{m}$.

\n

c)

\n

To find the tension, $T$ in Newtons, we resolve in the direction of motion, where $a=\\var{a}$ and $T$ is acting in the opposite direction.

\n

\\begin{align}
F & = ma \\\\
- T & = \\var{mass} \\times \\var{a} \\\\
T & = \\var{precround(mass*-a,3)}.
\\end{align}

\n

The tension in the rope is $\\var{precround(mass*-a,3)} \\ \\mathrm{N}$.

\n

d) 

\n

If the caravan experiences a resistance to motion of magnitude $\\var{resistance}N$ this resistance will act in the opposite direction to motion. 

\n

\\begin{align} F & = ma \\\\
                     - T - \\var{resistance} & = \\var{mass} \\times \\var{a}\\\\
                             T & = \\left(\\var{mass} \\times \\var{-a}\\right) - \\var{resistance} \\\\
                                & = \\var{precround(mass*-a - resistance,3)}. \\end{align}

\n

The tension in the rope is $\\var{precround(mass*-a-resistance,3)} \\ \\mathrm{N}$.

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A caravan of mass $\\var{mass} \\ \\mathrm{kg}$ is pulled on a rope by a car along a straight horizontal road. It decelerates at a constant rate of $\\var{-a} \\ \\mathrm{ms^{-2}}$ from an initial speed of $\\var{u} \\ \\mathrm{ms^{-1}}$. There is no resistance to motion.

\n

Give your answers to each of the following questions to 3 decimal places.

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3dp

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negative because deceleration

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initial speed

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