If the velocity of a particle is v = At + Bt2, where A and B are constants, then the distance travelled by it between Is and 2s is     [NEET 2016]

Velocity of the particle is given as v = At + Bt2where, A and B are constants.⇒    dxdt=At+Bt2                                                ∵v=dxdt⇒  dx=At+Bt2dtIntegrating both sides, we get               ∫x1x2dx=∫12At+Bt2dt⇒             Δx=x2-x1=A∫12tdt+B∫12t2dt                        =At2212+Bt3312                         =A222-12+B323-13∴   Distance travelled by the particle between Is and 2s is                    Δx=A2×(3)+B3(7)=3A2+7B3