[填空题]
Let $ f(t)=3 t^{2}+27$, where t>0 .
The graph of a function g is obtained when the graph of f is transformed by
a stretch by a scale of $\frac{1}{9}$ parallel to the y -axis, followed by a translation by the vector $\binom{4}{-5} $.
1. Find g(t) , giving your answer in the form $ a(t-b)^{2}+c$.
A particle moves along a straight line so that its velocity in $ \mathrm{m} \mathrm{s}^{-1}$ , at time t seconds, is given by g(t) .
2. Find the distance the particle travels between t=7 and t=10 .
