6 Two forces, \(\mathbf { P } = ( 6 \mathbf { i } - 3 \mathbf { j } )\) newtons and \(\mathbf { Q } = ( 3 \mathbf { i } + 15 \mathbf { j } )\) newtons, act on a particle. The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular.
- Find the resultant of \(\mathbf { P }\) and \(\mathbf { Q }\).
- Calculate the magnitude of the resultant of \(\mathbf { P }\) and \(\mathbf { Q }\).
- When these two forces act on the particle, it has an acceleration of \(( 1.5 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\). Find the mass of the particle.
- The particle was initially at rest at the origin.
- Find an expression for the position vector of the particle when the forces have been applied to the particle for \(t\) seconds.
- Find the distance of the particle from the origin when the forces have been applied to the particle for 2 seconds.