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## 'Dangerous Driver?' printed from http://nrich.maths.org/

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A particular speed camera is located a short distance down the road from a particular set of traffic lights, at which there is always a queue at rush hour. At around this time a driver was caught out by the camera and challenged the ticket in court, claiming that he started moving from rest at the lights and that it would be impossible to reach the speed shown on the ticket over the short distance between the lights and the speed camera.

Prosecutor: "Although I accept that you left the traffic lights at rest, you were snapped by the camera doing $133\mathrm{kmh}^{-1}$, which is found at a distance of $338$ metres from the traffic lights. I claim that this is ample distance to reach the speed shown on the ticket."

Defendant: "But the specifications in the manual of my cheap car show that the maximum acceleration is $0$ to $96\mathrm{kmh}^{-1}$ in $10.5\mathrm{s}$. I could never have accelerated to such a high speed in such a short distance!"

Analyse this case carefully. Could the penalty reasonably be rejected on mathematical grounds?