4 Two cars, P and Q, are being crashed as part of a film 'stunt'.
At the start

• P is travelling directly towards Q with a speed of \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\),
• Q is instantaneously at rest and has an acceleration of \(4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) directly towards P .

P continues with the same velocity and Q continues with the same acceleration. The cars collide \(T\) seconds after the start.

1. Find expressions in terms of \(T\) for how far each of the cars has travelled since the start. At the start, P is 90 m from Q .
2. Show that \(T ^ { 2 } + 4 T - 45 = 0\) and hence find \(T\).