2026 HGV P2 Q9

The velocity, \(v\) m/s, of a particle travelling in a straight line, \(t\) seconds after leaving a fixed point \(O\), is given by \(v=k(t^2-5t)\), where \(k\) is a constant.

The acceleration of the particle is 3 m/s² when \(t=3\).

1. Find the value of \(k\).[3]
2. Find the value of \(t\) when the particle first comes to instantaneously at rest.[2]
3. Show that the total distance covered by the particle during the first 10 seconds is 375 m.[5]