4. Geraint is a cyclist competing in a race along the Taff Trail. The Taff Trail is a track that runs from Cardiff Bay to Brecon. The chart below shows the altitude (height above sea level) along the route.
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\caption{Altitude Chart of the Taff Trail}
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\end{figure}
Geraint starts from rest at Cardiff Bay and has a speed of \(10 \mathrm {~ms} ^ { - 1 }\) when he crosses the finish line in Brecon. Geraint and his bike have a total mass of 80 kg . The resistance to motion may be modelled by a constant force of magnitude 16 N .
- Given that 1440 kJ of energy is used in overcoming resistances during the race,
- find the length of the track,
- calculate the work done by Geraint.
- The steepest section of the track may be modelled as a slope inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 2 } { 7 }\).
\includegraphics[max width=\textwidth, alt={}, center]{b6b77d92-acb6-4cc3-8328-1899ed4a87cd-5_513_844_1987_607}
Geraint is capable of producing a maximum power of 250 W . Find the maximum speed that Geraint can attain whilst travelling on this section of the track.