(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 ...
Question 1 Report
(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
Answer Details
(a) For parallelogram \(PQRS\) the diagonals bisect each other, so midpoint of \(PR\) = midpoint of \(QS\).
\[\left(\frac{-1+x}{2},\frac{4+y}{2}\right)=\left(\frac{2+(-2)}{2},\frac{3+3}{2}\right)=(0,3).\] \[\frac{-1+x}{2}=0\Rightarrow x=1,\qquad \frac{4+y}{2}=3\Rightarrow y=2.\]So \(R(1,2)\), i.e. \(x=1,\ y=2\). (Check: \(\vec{PQ}=(3,-1)=\vec{SR}\).)
(b) From rest, \(u=0\), reaches \(v=20\ \text{m/s}\) after \(s=8\ \text{m}\).
(i) Acceleration: \(v^2=u^2+2as\Rightarrow 20^2=2a(8)\Rightarrow a=\dfrac{400}{16}=25\ \text{m/s}^2\).
(ii) Time to travel 40 m: \(s=ut+\tfrac12 at^2\Rightarrow 40=\tfrac12(25)t^2=12.5t^2\).
\[t^2=3.2\Rightarrow t=\sqrt{3.2}\approx 1.79\ \text{s}.\]Download The App On Google Playstore
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