The initial velocity of an object is \(u = \begin{pmatrix} -5 \\ 3 \end{pmatrix} ms^{-1}\)....
FURTHER MATHEMATICS
WAEC 2010
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: C. \(\begin{pmatrix} 4 \\ -9 \end{pmatrix} ms^{-1}\)
Explanation
\(u = \begin{pmatrix} -5 \\ 3 \end{pmatrix} ms^{-1}\)
\(a = \begin{pmatrix} 3 \\ -4 \end{pmatrix} ms^{-2}; t = 3 secs\)
\(v = u + at \implies v = \begin{pmatrix} -5 \\ 3 \end{pmatrix} + \begin{pmatrix} 3 \\ -4 \end{pmatrix} \times 3\)
= \(\begin{pmatrix} -5 \\ 3 \end{pmatrix} + \begin{pmatrix} 9 \\ -12 \end{pmatrix} = \begin{pmatrix} 4 \\ -9 \end{pmatrix} ms^{-1}\)\)
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