If a grocery cart with a mass of 16.5 kg accelerates at +2.31 m/s2 against a frictional force of -15.0 N, what is the applied force?

Call the applied force 'A'. (Clever ?)The forces on the cart are  'A' forward and 15 N backward.The net force on the art is (A-15) forward.F = m aNet forward force = (mass of the cart) x (its forward acceleration)(A - 15) = (16.5) x (2.31)A - 15 = 38.115Add 15 to each side:A = 53.115 newtons

2th Law of Newton:[tex]\vec{R}=m.a\\
\\
\vec{R}=\vec{F} -\vec{F_a}=m.a\\
\\
\vec{F}-15=16.5*2.31\\
\\
\vec{F}=38.115+15\\
\\
\boxed{\vec{F}=53.115 \ N}[/tex]