Challenging +1.2 This is a first-order linear vector differential equation requiring an integrating factor method. While it involves vector notation and the integrating factor μ(t) = t^(-2), the technique is standard for M5/FP3 level. The solution process is methodical: find integrating factor, integrate both sides, apply initial condition. More challenging than routine mechanics but doesn't require novel insight—a well-prepared student would recognize the standard approach immediately.
A particle \(P\) moves in a plane such that its position vector \(\mathbf{r}\) metres at time \(t\) seconds \((t > 0)\) satisfies the differential equation
$$\frac{d\mathbf{r}}{dt} - \frac{2}{t}\mathbf{r} = 4i$$
When \(t = 1\), the particle is at the point with position vector \((i + j)\) m.
Find \(\mathbf{r}\) in terms of \(t\).
[9]
A particle $P$ moves in a plane such that its position vector $\mathbf{r}$ metres at time $t$ seconds $(t > 0)$ satisfies the differential equation
$$\frac{d\mathbf{r}}{dt} - \frac{2}{t}\mathbf{r} = 4i$$
When $t = 1$, the particle is at the point with position vector $(i + j)$ m.
Find $\mathbf{r}$ in terms of $t$.
[9]
\hfill \mbox{\textit{Edexcel M5 Q1 [9]}}