5 The constant forces \(\mathbf { F } _ { 1 } = ( 8 \mathbf { i } + 12 \mathbf { j } )\) newtons and \(\mathbf { F } _ { 2 } = ( 4 \mathbf { i } - 4 \mathbf { j } )\) newtons act on a particle. No other forces act on the particle.
- Find the resultant force acting on the particle.
- Given that the mass of the particle is 4 kg , show that the acceleration of the particle is \(( 3 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\).
- At time \(t\) seconds, the velocity of the particle is \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\).
- When \(t = 20 , \mathbf { v } = 40 \mathbf { i } + 32 \mathbf { j }\).
Show that \(\mathbf { v } = - 20 \mathbf { i } - 8 \mathbf { j }\) when \(t = 0\).
- Write down an expression for \(\mathbf { v }\) at time \(t\).
- Find the times when the speed of the particle is \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).