4 A ring is moving on a straight wire. Its velocity is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at time \(t\) seconds after passing a point Q .
Model A for the motion of the ring gives the velocity-time graph for \(0 \leqslant t \leqslant 6\) shown in Fig. 7 .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{196bd74f-c2b2-4cb3-b03c-8ecd9fce9c11-2_937_1414_325_404}
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\caption{Fig. 7}
\end{figure}
Use model A to calculate the following.
- The acceleration of the ring when \(t = 0.5\).
- The displacement of the ring from Q when
(A) \(t = 2\),
(B) \(t = 6\).
In an alternative model B , the velocity of the ring is given by \(v = 2 t ^ { 2 } - 14 t + 20\) for \(0 \leqslant t \leqslant 6\). - Calculate the acceleration of the ring at \(t = 0.5\) as given by model B.
- Calculate by how much the models differ in their values for the least \(v\) in the time interval \(0 \leqslant t \leqslant 6\).
- Calculate the displacement of the ring from Q when \(t = 6\) as given by model B .