7 A particle moves on a smooth horizontal surface with acceleration \(( 3 \mathbf { i } - 5 \mathbf { j } ) \mathrm { ms } ^ { - 2 }\). Initially the velocity of the particle is \(4 \mathbf { j } \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Find an expression for the velocity of the particle at time \(t\) seconds.
- Find the time when the particle is travelling in the \(\mathbf { i }\) direction.
- Show that when \(t = 4\) the speed of the particle is \(20 \mathrm {~ms} ^ { - 1 }\).