6. A particle moving in a straight line starts from rest at the point \(O\) at time \(t = 0\). At time \(t\) seconds, the velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) of the particle is given by $$\begin{aligned} & v = 3 t ( t - 4 ) , \quad 0 \leq t \leq 5
& v = 75 t ^ { - 1 } , \quad 5 \leq t \leq 10 \end{aligned}$$

1. Sketch a velocity-time graph for the particle for \(0 \leq t \leq 10\).
2. Find the set of values of \(t\) for which the acceleration of the particle is positive.
3. Show that the total distance travelled by the particle in the interval \(0 \leq t \leq 5\) is 39 m .
4. Find, to 3 significant figures, the value of \(t\) at which the particle returns to \(O\).