A particle $$\(P\)$$ moves in a straight line. It starts from rest at a point $$\(O\)$$ on the line and at time $$\(t\)$$ s after leaving $$\(O\)$$ it has acceleration $$\(a \mathrm{~m} \mathrm{~s}^{-2}\)$$, where $$\(a=6 t-18\)$$. Find the distance $$\(P\)$$ moves before it comes to instantaneous rest. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_w20_qp_41 Year：2020 Question No：4
Answer:
\({\left[v=3 t^{2}-18 t(+C)\right] }\)
\({\left[s=t^{3}-9 t^{2}(+C)\right] }\)
\(v=3 t^{2}-18 t\)
\(s=t^{3}-9 t^{2}\)
\(v=0,3 t^{2}-18 t=0 \quad[t=6]\)
\(s=6^{3}-9 \times 6^{2}-[0]\)
\(s=108 \mathrm{~m}\)
\({\left[s=t^{3}-9 t^{2}(+C)\right] }\)
\(v=3 t^{2}-18 t\)
\(s=t^{3}-9 t^{2}\)
\(v=0,3 t^{2}-18 t=0 \quad[t=6]\)
\(s=6^{3}-9 \times 6^{2}-[0]\)
\(s=108 \mathrm{~m}\)
Knowledge points:
4.2.3 use differentiation and integration with respect to time to solve simple problems concerning displacement, velocity and acceleration Calculus required is restricted to techniques from the content for Paper 1: Pure Mathematics 1.
Solution:
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