(a) P(-1, 4), Q(2, 3), R(x, y) and S(-2, 3) are the verticles of a parallelogram. Find the value of x and y.
(b) A particle starts from rest and moves in a straight line. It attains a velocity of 20ms(^{-1}) after travelling a distance of 8 metres. Calculate;
(ii) Iis acceleration
(ii) the time taken to travel 40 metres
Explanation
(over{PS}) = (over{OS}) – (over{OP}) = ((^{-2}_3)) – ((^{-1}_4)) = ((^{-1}_{-1}))
Similarly (over{QR}) = (over{OR}) – (over{OQ}) = ((^x_y)) – ((^2_3)) = ((^{x – 2}_{y – 3}))
Since (over{PS}) = (over{QR}), it flows that ((^{x – 2}_{y – 3})) = ((^{-1}_{-1})). Therefore, x – 2 = -1 which solved will yield x = 1.
Also, y – 3 = -1 which implies that y = 2
(b)(i), Since the particle starts from rest, the initial velocity (u) = 0 and substituting for final velocity (v) and distance (s) into the formula v(^2) = u(^2) + 2as to obtain 20(^2) = 0 + 2a(8) and when simplifies and solved for acceleration (a), to get a = 25ms(^{-2})
(b)(ii), S = ut + (frac{1}{2})at(^2), where s = 40, u = 0 and a = 25
Substituting these values into the equation we obtain 40 = 0 + (frac{1}{2}) x 25t(^2) and solving for t gave t = 1.79 seconds.