(a) Given that m = i - i, n = 2i + 3j and 2m + n - r = 0, find |r| (b) The distance, S metres of a moving particle at any time tseconds is given by S = 3t -...
Question 1 Report
(a) Given that m = i - i, n = 2i + 3j and 2m + n - r = 0, find |r|
(b) The distance, S metres of a moving particle at any time tseconds is given by
S = 3t - \(\frac{t^3}{3}\) + 9
Find the;
(i) time
(ii) distance travelled
When the particle is momentarily at rest
Answer Details
(a) Taking \(m=i-j\) and \(n=2i+3j\), with \(2m+n-r=0\) we get \(r=2m+n\).
\[r=2(i-j)+(2i+3j)=(2i-2j)+(2i+3j)=4i+j\]
\[|r|=\sqrt{4^{2}+1^{2}}=\sqrt{17}\approx4.12\]
(b) \(S=3t-\dfrac{t^{3}}{3}+9\). Velocity is \(v=\dfrac{dS}{dt}=3-t^{2}\).
(i) Time when momentarily at rest: \(v=0\):
\[3-t^{2}=0\ \Rightarrow\ t^{2}=3\ \Rightarrow\ t=\sqrt{3}\ \text{s}\ (\approx1.73\ \text{s})\]
(ii) Distance at that instant:
\[S=3\sqrt{3}-\frac{(\sqrt{3})^{3}}{3}+9=3\sqrt{3}-\sqrt{3}+9=2\sqrt{3}+9\approx12.46\ \text{m}\]
Download The App On Google Playstore
Everything you need to excel in your exams
