5
\includegraphics[max width=\textwidth, alt={}, center]{2b3457b6-1fe9-4e67-91d4-a8bc4a5b1709-3_394_789_251_639} The diagram shows the ( \(t , v\) ) graph of an athlete running in a straight line on a horizontal track in a 100 m race. He starts from rest and has constant acceleration until he reaches a speed of \(15 \mathrm {~ms} ^ { - 1 }\) when \(t = T\). He maintains this constant speed until he decelerates at a constant rate of \(1.75 \mathrm {~ms} ^ { - 2 }\) for the final 4 s of the race. He completes the race in 10 s .

1. Calculate \(T\). The athlete races against a robot which has a displacement from the starting line of \(\left( 3 t ^ { 2 } - 0.2 t ^ { 3 } \right) \mathrm { m }\), at time \(t \mathrm {~s}\) after the start of the race.
2. Show that the speed of the robot is \(15 \mathrm {~ms} ^ { - 1 }\) when \(t = 5\).
3. Find the value of \(t\) for which the decelerations of the robot and the athlete are equal.
4. Verify that the athlete and the robot reach the finish line simultaneously.