A particle \(P\) of mass 1.5 kg moves from rest at the origin such that at time \(t\) seconds it is subject to a single force of magnitude \(( 4 t + 3 ) \mathrm { N }\) in the direction of the positive \(x\)-axis.
Find the magnitude of the impulse exerted by the force during the interval \(1 \leq t \leq 4\).
Given that at time \(T\) seconds, \(P\) has a speed of \(22 \mathrm {~ms} ^ { - 1 }\),
find the value of \(T\) correct to 3 significant figures.