Standard +0.3 This is a straightforward M5 mechanics problem requiring application of Newton's second law and constant acceleration equations in 3D. Students must find the resultant force, calculate acceleration, determine displacement to find time, then use v = u + at. While it involves vectors and multiple steps, each step follows standard procedures with no conceptual challenges or novel problem-solving required.
At time \(t = 0\), a particle \(P\) of mass \(3\) kg is at rest at the point \(A\) with position vector \((j - 3k)\) m. Two constant forces \(\mathbf{F}_1\) and \(\mathbf{F}_2\) then act on the particle \(P\) and it passes through the point \(B\) with position vector \((8i - 3j + 5k)\) m.
Given that \(\mathbf{F}_1 = (4i - 2j + 5k)\) N and \(\mathbf{F}_2 = (8i - 4j + 7k)\) N and that \(\mathbf{F}_1\) and \(\mathbf{F}_2\) are the only two forces acting on \(P\), find the velocity of \(P\) as it passes through \(B\), giving your answer as a vector.
[7]
At time $t = 0$, a particle $P$ of mass $3$ kg is at rest at the point $A$ with position vector $(j - 3k)$ m. Two constant forces $\mathbf{F}_1$ and $\mathbf{F}_2$ then act on the particle $P$ and it passes through the point $B$ with position vector $(8i - 3j + 5k)$ m.
Given that $\mathbf{F}_1 = (4i - 2j + 5k)$ N and $\mathbf{F}_2 = (8i - 4j + 7k)$ N and that $\mathbf{F}_1$ and $\mathbf{F}_2$ are the only two forces acting on $P$, find the velocity of $P$ as it passes through $B$, giving your answer as a vector.
[7]
\hfill \mbox{\textit{Edexcel M5 Q1 [7]}}