- A particle \(P\) moves with acceleration \(( 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { ms } ^ { - 2 }\)
At time \(t = 0 , P\) is moving with velocity \(( - 2 \mathbf { i } + 2 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\)
- Find the velocity of \(P\) at time \(t = 2\) seconds.
At time \(t = 0 , P\) passes through the origin \(O\).
At time \(t = T\) seconds, where \(T > 0\), the particle \(P\) passes through the point \(A\).
The position vector of \(A\) is ( \(\lambda \mathbf { i } - 4.5 \mathbf { j }\) )m relative to \(O\), where \(\lambda\) is a constant. - Find the value of \(T\).
- Hence find the value of \(\lambda\)