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\includegraphics[max width=\textwidth, alt={}, center]{a92f97e2-343f-4cac-ae38-f18a4ad49055-3_574_1205_260_470} The diagram shows a velocity-time graph which models the motion of a cyclist. The graph consists of five straight line segments. The cyclist accelerates from rest to a speed of \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) over a period of 10 s , and then travels at this speed for a further 20 s . The cyclist then descends a hill, accelerating to speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) over a period of 10 s . This speed is maintained for a further 30 s . The cyclist then decelerates to rest over a period of 20 s .

1. Find the acceleration of the cyclist during the first 10 seconds.
2. Show that the total distance travelled by the cyclist in the 90 seconds of motion may be expressed as \(( 45 V + 150 ) \mathrm { m }\). Hence find \(V\), given that the total distance travelled by the cyclist is 465 m .
3. The combined mass of the cyclist and the bicycle is 80 kg . The cyclist experiences a constant resistance to motion of 20 N . Use an energy method to find the vertical distance which the cyclist descends during the downhill section from \(t = 30\) to \(t = 40\), assuming that the cyclist does no work during this time.