WAEC 2019 · Paper 2 · Q14

(a)
$P(-1, 4)$ , $Q(2, 3)$ , $R(x, y)$ and $S(-2, 3)$ are the vertices of a parallelogram. Find the values of $x$ and $y$ .
Separate values with commas, e.g. 3, −2
(b)
A particle starts from rest and moves in a straight line. It attains a velocity of $20\text{ m s}^{-1}$ after travelling a distance of 8 metres. Calculate: (i) its acceleration; (ii) the time taken to travel 40 metres.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

In $PQRS$ , $\overrightarrow{QR} = \overrightarrow{PS}$
$= \begin{pmatrix} -2 + 1 \\ 3 - 4 \end{pmatrix}$
$= \begin{pmatrix} -1 \\ -1 \end{pmatrix}$ .
So $R = (2 - 1, 3 - 1) = (1, 2)$ : $x = 1$ and $y = 2$ .

(b)(i)

$v^2 = u^2 + 2as$ : $400 = 0 + 16a$ , so $a = 25\text{ m s}^{-2}$ .

(ii)

$s = ut + \frac12at^2$ : $40 = \frac{25}{2}t^2$ , so $t^2 = 3.2$ and $t \approx 1.79\text{ s}$ .

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