6 A particle moves in a straight line $$\(A B\)$$. The velocity $$\(v \mathrm{~m} \mathrm{~s}^{-1}\)$$ of the particle $$\(t \mathrm{~s}\)$$ after leaving $$\(A\)$$ is given by $$\(v=k\left(t^{2}-10 t+21\right)\)$$, where $$\(k\)$$ is a constant. The displacement of the particle from $$\(A\)$$, in the direction towards $$\(B\)$$, is $$\(2.85 \mathrm{~m}\)$$ when $$\(t=3\)$$ and is $$\(2.4 \mathrm{~m}\)$$ when $$\(t=6\)$$. Find the value of $$\(k\)$$. Hence find an expression, in terms of $$\(t\)$$, for the displacement of the particle from $$\(A\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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