9709 P43 - Jun 2023 - Q5 - 10 marks
3742
Take \(g=10\,\mathrm{m\,s^{-2}}\).
A particle starts from rest at \(O\) and moves in a straight line. Its acceleration is \(a=k\sqrt t\,\mathrm{m\,s^{-2}}\) for \(0\le t\le9\), with constant \(k\). Its velocity at \(t=9\) is \(1.8\,\mathrm{m\,s^{-1}}\).
(a) Show \(k=0.1\). [3]
For \(t>9\), its velocity is \(v=0.2(t-9)^2+1.8\,\mathrm{m\,s^{-1}}\).
(b) Show that the distance in the first 9 s is one tenth of the distance from t=9 to t=18. [4]
(c) Find the greatest acceleration during the first 10 s. [3]
