A particle P P\,P moves along the xxx-axis.
At time t t\,t seconds, t≥0t \geq 0t≥0, the acceleration of P P\,P is (3t+5)(3t + 5)(3t+5) m s−2^{-2}−2 measured in the positive x x\,x direction.
When t=0t = 0t=0 the velocity of P P\,P is 2 m s−1^{-1}−1 in the positive x x\,x direction.
When t=Tt = Tt=T the velocity of P P\,P is 6 m s−1^{-1}−1 in the positive x x\,x direction.
Find the value of TTT.