Edexcel M2 2004 January — Question 2 9 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2004
SessionJanuary
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicImpulse and momentum (advanced)
TypeVelocity after impulse (direct calculation)
DifficultyStandard +0.3 This is a straightforward M2 mechanics question requiring differentiation to find force from velocity (F=ma), then applying impulse-momentum theorem with vector addition. All steps are standard procedures with no novel problem-solving required, making it slightly easier than average.
Spec1.10b Vectors in 3D: i,j,k notation3.03a Force: vector nature and diagrams3.03c Newton's second law: F=ma one dimension6.03e Impulse: by a force6.03f Impulse-momentum: relation

2. A particle \(P\) of mass 0.75 kg is moving under the action of a single force \(\mathbf { F }\) newtons. At time \(t\) seconds, the velocity \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\) of \(P\) is given by $$\mathbf { v } = \left( t ^ { 2 } + 2 \right) \mathbf { i } - 6 t \mathbf { j }$$
  1. Find the magnitude of \(\mathbf { F }\) when \(t = 4\).
    (5) When \(t = 5\), the particle \(P\) receives an impulse of magnitude \(9 \sqrt { } 2 \mathrm { Ns }\) in the direction of the vector \(\mathbf { i } - \mathbf { j }\).
  2. Find the velocity of \(P\) immediately after the impulse.

2. A particle $P$ of mass 0.75 kg is moving under the action of a single force $\mathbf { F }$ newtons. At time $t$ seconds, the velocity $\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }$ of $P$ is given by

$$\mathbf { v } = \left( t ^ { 2 } + 2 \right) \mathbf { i } - 6 t \mathbf { j }$$
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of $\mathbf { F }$ when $t = 4$.\\
(5)

When $t = 5$, the particle $P$ receives an impulse of magnitude $9 \sqrt { } 2 \mathrm { Ns }$ in the direction of the vector $\mathbf { i } - \mathbf { j }$.
\item Find the velocity of $P$ immediately after the impulse.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2004 Q2 [9]}}