Edexcel M2 — Question 3 10 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Marks10
PaperDownload PDF ↗
TopicVariable acceleration (1D)
TypeForce from vector acceleration
DifficultyStandard +0.3 This is a straightforward M2 mechanics question requiring standard techniques: differentiate velocity to find acceleration, apply F=ma, find magnitude of a vector, and integrate velocity to find displacement. All steps are routine applications of learned procedures with no novel problem-solving required, making it slightly easier than average.
Spec1.10h Vectors in kinematics: uniform acceleration in vector form3.02a Kinematics language: position, displacement, velocity, acceleration3.02b Kinematic graphs: displacement-time and velocity-time3.03d Newton's second law: 2D vectors

A particle \(P\) of mass \(0.3\) kg is moving under the action of a single force \(F\) newtons. At time \(t\) seconds the velocity of \(P\), v m s\(^{-1}\), is given by $$\mathbf{v} = 3t^2\mathbf{i} + (6t - 4)\mathbf{j}.$$
  1. Calculate, to 3 significant figures, the magnitude of \(\mathbf{F}\) when \(t = 2\). [5]
When \(t = 0\), \(P\) is at the point \(A\). The position vector of \(A\) with respect to a fixed origin \(O\) is \((3\mathbf{i} - 4\mathbf{j})\) m. When \(t = 4\), \(P\) is at the point \(B\).
  1. Find the position vector of \(B\). [5]

A particle $P$ of mass $0.3$ kg is moving under the action of a single force $F$ newtons. At time $t$ seconds the velocity of $P$, v m s$^{-1}$, is given by

$$\mathbf{v} = 3t^2\mathbf{i} + (6t - 4)\mathbf{j}.$$

\begin{enumerate}[label=(\alph*)]
\item Calculate, to 3 significant figures, the magnitude of $\mathbf{F}$ when $t = 2$.
[5]
\end{enumerate}

When $t = 0$, $P$ is at the point $A$. The position vector of $A$ with respect to a fixed origin $O$ is $(3\mathbf{i} - 4\mathbf{j})$ m. When $t = 4$, $P$ is at the point $B$.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the position vector of $B$.
[5]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2  Q3 [10]}}