5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{84c0eead-0a87-4d87-b33d-794a94bb466c-14_117_1393_328_337}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Three points \(P , Q\) and \(R\) are on a horizontal road where \(P Q R\) is a straight line.
The point \(Q\) is between \(P\) and \(R\), with \(P Q = 6 x\) metres and \(Q R = 5 x\) metres, as shown in Figure 2.
A vehicle moves along the road from \(P\) to \(Q\) with constant acceleration.
The vehicle is modelled as a particle.
At time \(t = 0\), the vehicle passes \(P\) with speed \(u \mathrm {~ms} ^ { - 1 }\)
At time \(t = 12 \mathrm {~s}\), the vehicle passes \(Q\) with speed \(2 u \mathrm {~ms} ^ { - 1 }\)
Using the model,
- show that \(x = 3 u\)
As the vehicle passes \(Q\), the acceleration of the vehicle changes instantaneously to \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)
The vehicle continues to move with a constant acceleration of \(1.5 \mathrm {~ms} ^ { - 2 }\) and passes \(R\) with speed \(3 u \mathrm {~ms} ^ { - 1 }\)
Using the model,
- find the value of \(u\),
- find the distance travelled by the vehicle during the first 14 seconds after passing \(P\)