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\includegraphics[max width=\textwidth, alt={}, center]{57725055-7bce-4ad0-bb1c-59d07d56e2bd-4_531_1481_1194_331} A sprinter \(S\) starts from rest at time \(t = 0\), where \(t\) is in seconds, and runs in a straight line. For \(0 \leqslant t \leqslant 3 , S\) has velocity \(\left( 6 t - t ^ { 2 } \right) \mathrm { m } \mathrm { s } ^ { - 1 }\). For \(3 < t \leqslant 22 , S\) runs at a constant speed of \(9 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). For \(t > 22 , S\) decelerates at \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) (see diagram).

1. Express the acceleration of \(S\) during the first 3 seconds in terms of \(t\).
2. Show that \(S\) runs 18 m in the first 3 seconds of motion.
3. Calculate the time \(S\) takes to run 100 m .
4. Calculate the time \(S\) takes to run 200 m . OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright Acknowledgements Booklet. This is produced for each series of examinations, is given to all schools that receive assessment material and is freely available to download from our public website (\href{http://www.ocr.org.uk}{www.ocr.org.uk}) after the live examination series.
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