Question

\begin{tabular}{|c|c|c|c|c|c|} \hline\( t \) & 1 & 4 & 6 & 7 & 11 \\ \hline\( x_{p}(t) \) & -3 & 12 & 9 & 0 & 1 \\ \hline\( v_{p}(t) \) & 2 & 5 & -8 & -1 & 3 \\ \hline \end{tabular} 3. For \( 0 \leq t \leq 11 \), particles \( P \) and \( Q \) are moving along the \( x \) axis. The positions of the particles are \( x_{P} \) and \( x_{Q} \) respectively. Selected values of the position and velocity for particle \( P \) are given in the table above along with a graph of the velocity for particle \( Q \). It is known that \( x_{Q}(6)=5 \). (a) Approximate \( a_{P}(5) \). Show the calculations that lead to your answer. (b) Find \( a_{Q}(\pi) \). (c) At what time(s) \( t \) does particle \( Q \) turn around? Give a reason for your answer. (d) Are particles \( P \) and \( Q \) moving toward or away from each other at time \( t=6 \) ? Give a reason for your answer. (e) Is particle \( Q \) speeding up or slowing down when \( t=1 \) ? Give a reason for your answer. (f) Can you guarantee a time \( c \), where \( 1<c<11 \), such that \( v_{P}(c)=0 \) ? Justify your answer. g) What is the velocity of particle \( Q \) when \( x_{P}(t)=9 \) ?

          \begin{tabular}{|c|c|c|c|c|c|}
\hline\( t \) & 1 & 4 & 6 & 7 & 11 \\
\hline\( x_{p}(t) \) & -3 & 12 & 9 & 0 & 1 \\
\hline\( v_{p}(t) \) & 2 & 5 & -8 & -1 & 3 \\
\hline
\end{tabular}
3. For \( 0 \leq t \leq 11 \), particles \( P \) and \( Q \) are moving along the \( x \) axis. The positions of the particles are \( x_{P} \) and \( x_{Q} \) respectively. Selected values of the position and velocity for particle \( P \) are given in the table above along with a graph of the velocity for particle \( Q \). It is known that \( x_{Q}(6)=5 \).
(a) Approximate \( a_{P}(5) \). Show the calculations that lead to your answer.
(b) Find \( a_{Q}(\pi) \).
(c) At what time(s) \( t \) does particle \( Q \) turn around? Give a reason for your answer.
(d) Are particles \( P \) and \( Q \) moving toward or away from each other at time \( t=6 \) ? Give a reason for your answer.
(e) Is particle \( Q \) speeding up or slowing down when \( t=1 \) ? Give a reason for your answer.
(f) Can you guarantee a time \( c \), where \( 1<c<11 \), such that \( v_{P}(c)=0 \) ? Justify your answer.
g) What is the velocity of particle \( Q \) when \( x_{P}(t)=9 \) ?

t 1 4 6 7 11

xp(t) -3 12 9 0 1

vp(t) 2 5 -8 -1 3

3. For 0 ≤ t ≤ 11, particles P and Q are moving along the x axis. The positions of the particles are xP and xQ respectively. Selected values of the position and velocity for particle P are given in the table above along with a graph of the velocity for particle Q. It is known that xQ(6)=5.
(a) Approximate aP(5). Show the calculations that lead to your answer.
(b) Find aQ(π).
(c) At what time(s) t does particle Q turn around? Give a reason for your answer.
(d) Are particles P and Q moving toward or away from each other at time t=6 ? Give a reason for your answer.
(e) Is particle Q speeding up or slowing down when t=1 ? Give a reason for your answer.
(f) Can you guarantee a time c, where 1<c<11, such that vP(c)=0 ? Justify your answer.
g) What is the velocity of particle Q when xP(t)=9 ?

Added by Steven I.

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