Further Mathematics Past Questions and Answers

A body starts from rest and moves in a straight line with uniform acceleration of \(5 ms^{-2}\). How far, in metres, does it go in 10 seconds?

If n items are arranged two at a time, the number obtained is 20. Find the value of n.

If \(p = \begin{pmatrix} 2 \\ -2 \end{pmatrix} \) and \(q = \begin{pmatrix} 3 \\ 4 \end{pmatrix}\), find \(|q - \frac{1}{2}p|\).

Find the value of the constant k for which \(a = 4 i - k j\) and \(b = 3 i + 8 j\) are perpendicular.

The initial and final velocities of an object of mass 5 kg are \(u = \begin{pmatrix} 1 \\ 3 \end{pmatrix}\) and \(v = \begin{pmatrix} 4 \\ 7 \end{pmatrix}\) respectively. Find the magnitude of its change in momentum.