A particle moves along a straight line. The fixed point $$\(O\)$$ lies on this line. The displacement of the particle from $$\(O\)$$ at time $$\(t\)$$ seconds, $$\(t \geqslant 0\)$$, is $$\(s\)$$ metres where $$\[ s=t^{3}+4 t^{2}-5 t+7 \]$$ At time $$\(T\)$$ seconds the velocity of $$\(P\)$$ is $$\(V \mathrm{~m} / \mathrm{s}\)$$ where $$\(V \geqslant-5\)$$ Find an expression for $$\(T\)$$ in terms of $$\(V\)$$. Give your expression in the form $$\(\frac{-4+\sqrt{k+m V}}{3}\)$$ where $$\(k\)$$ and $$\(m\)$$ are integers to be found. $$\(T=\)$$

Answer:

Knowledge points:

Solution: