- \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular horizontal unit vectors.]
A particle \(P\) is moving with constant acceleration. At 2 pm , the velocity of \(P\) is \(( 3 \mathbf { i } + 5 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\) and at 2.30 pm the velocity of \(P\) is \(( \mathbf { i } + 7 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\)
At time \(T\) hours after \(2 \mathrm { pm } , P\) is moving in the direction of the vector \(( - \mathbf { i } + 2 \mathbf { j } )\)
- Find the value of \(T\).
Another particle, \(Q\), has velocity \(\mathbf { v } _ { Q } \mathrm {~km} \mathrm {~h} ^ { - 1 }\) at time \(t\) hours after 2 pm , where
$$\mathbf { v } _ { Q } = ( - 4 - 2 t ) \mathbf { i } + ( \mu + 3 t ) \mathbf { j }$$
and \(\mu\) is a constant.
Given that there is an instant when the velocity of \(P\) is equal to the velocity of \(Q\),
- find the value of \(\mu\).