Edexcel M2 2015 June — Question 6 11 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2015
SessionJune
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVariable acceleration (1D)
TypeTotal distance with direction changes
DifficultyStandard +0.3 This is a straightforward M2 mechanics question requiring standard techniques: (a) solving a quadratic equation when v=0, (b) differentiating velocity to find acceleration, (c) integrating velocity with attention to sign changes. While multi-part, each step uses routine methods with no novel insight required, making it slightly easier than average.
Spec3.02a Kinematics language: position, displacement, velocity, acceleration3.02f Non-uniform acceleration: using differentiation and integration

  1. A particle \(P\) moves on the positive \(x\)-axis. The velocity of \(P\) at time \(t\) seconds is \(\left( 2 t ^ { 2 } - 9 t + 4 \right) \mathrm { m } \mathrm { s } ^ { - 1 }\). When \(t = 0 , P\) is 15 m from the origin \(O\).
Find
  1. the values of \(t\) when \(P\) is instantaneously at rest,
  2. the acceleration of \(P\) when \(t = 5\)
  3. the total distance travelled by \(P\) in the interval \(0 \leqslant t \leqslant 5\)

\begin{enumerate}
  \item A particle $P$ moves on the positive $x$-axis. The velocity of $P$ at time $t$ seconds is $\left( 2 t ^ { 2 } - 9 t + 4 \right) \mathrm { m } \mathrm { s } ^ { - 1 }$. When $t = 0 , P$ is 15 m from the origin $O$.
\end{enumerate}

Find\\
(a) the values of $t$ when $P$ is instantaneously at rest,\\
(b) the acceleration of $P$ when $t = 5$\\
(c) the total distance travelled by $P$ in the interval $0 \leqslant t \leqslant 5$

\hfill \mbox{\textit{Edexcel M2 2015 Q6 [11]}}