Given ( a(t) = \fracdvdt = 6t + 4 ). Integrate: [ v(t) = \int (6t + 4) , dt = 3t^2 + 4t + C_1 ] Using ( v(0)=5 ): ( 5 = 0 + 0 + C_1 \implies C_1 = 5 ). Thus, ( v(t) = 3t^2 + 4t + 5 ).
Therefore, ( s(t) = t^3 + 2t^2 + 5t + 2 ) meters. rectilinear motion problems and solutions mathalino upd
[ v(2) = 3(4) - 12(2) + 9 = 12 - 24 + 9 = -3 \ \textm/s ] [ a(2) = 6(2) - 12 = 0 \ \textm/s^2 ] Given ( a(t) = \fracdvdt = 6t + 4 )
Find when ( v(t)=0 ): ( 2t-4=0 \implies t=2 ) s. rectilinear motion problems and solutions mathalino upd