1 The velocity of a particle at time \(t\) seconds is \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\), where
$$\mathbf { v } = \left( 4 + 3 t ^ { 2 } \right) \mathbf { i } + ( 12 - 8 t ) \mathbf { j }$$
- When \(t = 0\), the particle is at the point with position vector \(( 5 \mathbf { i } - 7 \mathbf { j } ) \mathrm { m }\).
Find the position vector, \(\mathbf { r }\) metres, of the particle at time \(t\).
- Find the acceleration of the particle at time \(t\).
- The particle has mass 2 kg .
Find the magnitude of the force acting on the particle when \(t = 1\).