16 An elite athlete runs in a straight line to complete a 100-metre race.
During the race, the athlete's velocity, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), may be modelled by
$$v = 11.71 - 11.68 \mathrm { e } ^ { - 0.9 t } - 0.03 \mathrm { e } ^ { 0.3 t }$$
where \(t\) is the time, in seconds, after the starting pistol is fired.
16
- Find the maximum value of \(v\), giving your answer to one decimal place.
Fully justify your answer.
16 - Find an expression for the distance run in terms of \(t\).
[0pt]
[6 marks]
16 - The athlete's actual time for this race is 9.8 seconds.
Comment on the accuracy of the model.
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