1.
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\caption{Figure 1}
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Two children, Pat \(( P )\) and Sam \(( S )\), run a race along a straight horizontal track.
Both children start from rest at the same time and cross the finish line at the same time.
In a model of the motion:
Pat accelerates at a constant rate from rest for 5 s until reaching a speed of \(4 \mathrm {~ms} ^ { - 1 }\) and then maintains a constant speed of \(4 \mathrm {~ms} ^ { - 1 }\) until crossing the finish line.
Sam accelerates at a constant rate of \(1 \mathrm {~ms} ^ { - 2 }\) from rest until reaching a speed of \(X \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and then maintains a constant speed of \(X \mathrm {~m} \mathrm {~s} ^ { - 1 }\) until crossing the finish line.
Both children take 27.5 s to complete the race.
The velocity-time graphs shown in Figure 1 describe the model of the motion of each child from the instant they start to the instant they cross the finish line together.
Using the model,
- explain why the areas under the two graphs are equal,
- find the acceleration of Pat during the first 5 seconds,
- find, in metres, the length of the race,
- find the value of \(X\), giving your answer to 3 significant figures.