2020 NOV Afternoon P1 Q7

Consider two particles, \(P_1\) and \(P_2\), which start to move at the same time.
Particle \(P_1\) moves in a straight line such that its displacement from a fixed-point is given by \(s(t) = 10 -\frac{7}{4}t^2\), for \( t \geq 0\).

1. Find an expression for the velocity of \(P_1\) at the time \(t\).

   [2]

Particle \(P_2\) also moves in a straight line. The position of \(P_2\) is given by \(\mathbf{r} = \begin{pmatrix}-1 \\ \ 6 \end{pmatrix} + t \begin{pmatrix} 4 \\ -3 \end{pmatrix}\).
The speed of \(P_1\) is greater than the speed of \(P_2\) when \(t > q\).

2. Find the value of \(q\).

   [5]