- A physics student is studying the movement of particles in an electric field. In one experiment, the distances in micrometres of two moving particles, \(A\) and \(B\), from a fixed point \(O\) are modelled by
$$\begin{aligned}
& d _ { A } = | 5 t - 31 |
& d _ { B } = \left| 3 t ^ { 2 } - 25 t + 8 \right|
\end{aligned}$$
respectively, where \(t\) is the time in seconds after motion begins.
- Use algebra to find the range of time for which particle \(A\) is further away from \(O\) than particle \(B\) is from \(O\).
It was recorded that the distance of particle \(B\) from \(O\) was less than the distance of particle \(A\) from \(O\) for approximately 4 seconds.
- Use this information to assess the validity of the model.