In an experiment to improve road safety, the following information was gathered about the braking di

Question

In an experiment to improve road safety, the following information was gathered about the braking distance $d$, measured in feet, for a car travelling at different velocities $v$, measured in miles per hour. $v$$10$$20$$30$$40$$50$$60$$70$$80$ $d$$27$$58$$97$$155$$212$$308$$399$$516$ Draw a scatter diagram for these values, labelling the axes.[1] By calculating the relevant product moment correlation coefficients, determine whether the relationship between $v$ and $d$ is modelled better by $d=av+b$ or by $\ln d=av+b$. Explain how you decide which model is better, and state the equation in this case.[4] Use your equation found in part (ii) to estimate the braking distance when the car is travelling at $64$ miles per hour. Explain whether your estimate is reliable.[2] Scientists from another country wish to apply the model, but the measured velocity of the car was recorded as $m$ kilometres per hour instead. Given that $1$ kilometre $=0.621$ miles, re-write your equation in part (ii) in terms of $d$ and $m$ so that it can be used to estimate the braking distance for a given value of $m$.[2]

Accepted Answer

(ii) ${\ln d = 0.0406v + 3.21}$ (${3}$ s.f) (iii) ${d = 332.85}$ (${5}$ s.f.) The estimated braking distance is ${333}$ feet. Since ${r}$ is close to ${1}$ and ${v = 64}$ is within the given data range of ${v\ (10 \leq v \leq 80)}$, the estimate is reliable. (iv) ${\ln d = 0.0252m + 3.21}$ (${3}$ s.f)

2023 MI P2 Q10

2023 MI P2 Q10

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