5. Two flies \(P\) and \(Q\), are crawling vertically up a wall. At time \(t = 0\), the flies are at the same height above the ground, with \(P\) crawling at a steady speed of \(4 \mathrm { cms } ^ { - 1 }\).
\(Q\) starts from rest at time \(t = 0\) and accelerates uniformly to a speed of \(6 \mathrm {~cm} \mathrm {~s} ^ { - 1 }\) in 6 seconds. Fly \(Q\) then maintains this speed.
- Find the value of \(t\) when the two flies are moving at the same speed.
- Sketch on the same diagram, speed-time graphs to illustrate the motion of the two flies.
Given that the distance of the two flies from the top of the wall at time \(t = 0\) is \(x \mathrm {~cm}\) and that \(Q\) reaches the top of the wall first,
- show that \(x > 36\).