An athlete goes for a run along a straight horizontal road. Starting from rest, she accelerates at \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) up to a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). She then maintains this constant speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) before finally decelerating at \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) back to rest. She covers a total distance of 1500 m in 270 s .
Sketch a speed-time graph to represent the athlete's run.
Show that she accelerates for \(\frac { 5 V } { 3 }\) seconds.
Show that \(V ^ { 2 } - k V + 450 = 0\), where \(k\) is a constant to be found.