3 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.
- 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 \(Q\).
Show that \(T ^ { 2 } + 4 T - 45 = 0\) and hence find \(T\).