2026 CSS P2 Q11

A particle moves in a straight line and passes a fixed point \(O\) with a velocity of \(-8\) m/s. Its acceleration, \(a\) m/s\(^2\), \(t\) seconds after passing \(O\) is given by \(a=6-2t\).

Find

1. an expression for the velocity of the particle after \(t\) seconds,[2]
2. the maximum velocity of the particle,[3]
3. the value(s) of \(t\) when the particle is instantaneously at rest,[2]
4. the distance travelled by the particle in the first 8 seconds of its motion.[4]