Edexcel M2 2021 June — Question 2 8 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2021
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVariable acceleration (vectors)
TypeFind force using F=ma
DifficultyStandard +0.3 This is a straightforward M2 mechanics question requiring differentiation of velocity to find acceleration, then applying F=ma, followed by integration and solving when the i-component equals zero. All steps are routine applications of standard techniques with no novel problem-solving required, making it slightly easier than average.
Spec3.02f Non-uniform acceleration: using differentiation and integration3.03d Newton's second law: 2D vectors

2. A particle \(P\) of mass 1.5 kg moves under the action of a single force \(\mathbf { F }\) newtons. At time \(t\) seconds, \(t \geqslant 0 , P\) has velocity \(\mathbf { v } \mathrm { ms } ^ { - 1 }\), where $$\mathbf { v } = \left( 5 t ^ { 2 } - t ^ { 3 } \right) \mathbf { i } + \left( 2 t ^ { 3 } - 8 t \right) \mathbf { j }$$
  1. Find \(\mathbf { F }\) when \(t = 2\) At time \(t = 0 , P\) is at the origin \(O\).
  2. Find the position vector of \(P\) relative to \(O\) at the instant when \(P\) is moving in the direction of the vector \(\mathbf { j }\)

2. A particle $P$ of mass 1.5 kg moves under the action of a single force $\mathbf { F }$ newtons.

At time $t$ seconds, $t \geqslant 0 , P$ has velocity $\mathbf { v } \mathrm { ms } ^ { - 1 }$, where

$$\mathbf { v } = \left( 5 t ^ { 2 } - t ^ { 3 } \right) \mathbf { i } + \left( 2 t ^ { 3 } - 8 t \right) \mathbf { j }$$
\begin{enumerate}[label=(\alph*)]
\item Find $\mathbf { F }$ when $t = 2$

At time $t = 0 , P$ is at the origin $O$.
\item Find the position vector of $P$ relative to $O$ at the instant when $P$ is moving in the direction of the vector $\mathbf { j }$
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2021 Q2 [8]}}