The initial velocity of an object is \(u = \begin{pmatrix} -5 \\ 3 \end{pmatrix} ms^{-1}\). If the acceleration of the object is \(a = \begin{pmatrix} 3 \\ -4 \end{pmatrix} ms^{-2}\) and it moved for 3 seconds, find the final velocity.

A.

\(\begin{pmatrix} -14 \\ 15 \end{pmatrix} ms^{-1}\)

B.

\(\begin{pmatrix} -2 \\ 1 \end{pmatrix} ms^{-1}\)

C.

\(\begin{pmatrix} 4 \\ -9 \end{pmatrix} ms^{-1}\)

D.

\(\begin{pmatrix} 14 \\ -9 \end{pmatrix} ms^{-1}\)

Correct answer is C

\(u = \begin{pmatrix} -5 \\ 3 \end{pmatrix} ms^{-1}\)

\(a = \begin{pmatrix} 3 \\ -4 \end{pmatrix} ms^{-2}; t = 3 secs\)

\(v = u + at \implies v = \begin{pmatrix} -5 \\ 3 \end{pmatrix} + \begin{pmatrix} 3 \\ -4 \end{pmatrix} \times 3\)

= \(\begin{pmatrix} -5 \\ 3 \end{pmatrix} + \begin{pmatrix} 9 \\ -12 \end{pmatrix} = \begin{pmatrix} 4 \\ -9 \end{pmatrix} ms^{-1}\)\)