Newton's Second Law

F_net = ma is a statement about cause and effect. Forces don't directly set velocity, they set acceleration — the rate velocity changes. Push a shopping cart with 20 N and it leaps forward because its mass is tiny. Push a parked car with that same 20 N and it barely creeps, because the mass is huge and a = F_net/m shrinks accordingly. Same cause, wildly different effect, because mass is the resistance term in the equation.

Direction matters as much as size. Acceleration is a vector that points exactly where the net force vector points, no matter which way the object is already moving. Add up every force acting on the object as vectors first, then divide by mass. If forces fight each other, like a car's engine pushing forward while drag pushes back, you subtract their magnitudes along that line to get the net force, then find acceleration from that net value — not from either force alone. That's why a 1200 kg car with 3600 N forward and 900 N drag accelerates at (3600-900)/1200 = 2.25 m/s², forward.

This law is the engine of every dynamics problem in the unit: once you can find net force from a free body diagram, F_net = ma hands you acceleration, and acceleration integrates into velocity and position. It also explains the baseball case: stopping a 0.145 kg ball from 40 m/s in 0.01 s needs F = m(delta v)/t = 0.145 x 40 / 0.01 = 580 N, a huge average force because the time is so short. The same logic sets up momentum and impulse, which rewrite F = ma over time instead of distance.