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a)

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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 $v^2=u^2+2as$.

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\\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}

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

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b)

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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.

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\\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 $\\var{s} \\, \\mathrm{m}$.

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c)

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

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\\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 $\\var{precround(mass*-a,3)} \\ \\mathrm{N}$.

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d) 

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

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\\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 $\\var{precround(mass*-a-resistance,3)} \\ \\mathrm{N}$.

", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "

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

", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "(u^2+2*a*s)^(1/2)", "minValue": "(u^2+2*a*s)^(1/2)", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "

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.

", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "-(mass*a)", "minValue": "-(mass*a)", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "

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 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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negative because deceleration

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3dp

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initial speed

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

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