- A particle \(P\) moves along a straight line such that at time \(t\) seconds, \(t \geqslant 0\), after leaving the point \(O\) on the line, the velocity, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), of \(P\) is modelled as
$$v = ( 7 - 2 t ) ( t + 2 )$$
- Find the value of \(t\) at the instant when \(P\) stops accelerating.
- Find the distance of \(P\) from \(O\) at the instant when \(P\) changes its direction of motion.
In this question, solutions relying on calculator technology are not acceptable.