Newton's Second Law

Newton's second law says that the acceleration of an object is proportional to the net force on it and inversely proportional to its mass. Push twice as hard and it speeds up twice as fast; make it twice as heavy and it speeds up half as fast. The equation also defines the unit: one newton is exactly the force that accelerates one kilogram at one metre per second squared, so $1\ \text{N} = 1\ \text{kg·m/s}^2$. Newton himself did not write $F = ma$; he wrote that force is the rate of change of momentum, $F = \mathrm{d}p/\mathrm{d}t$, which is the more general statement and reduces to $ma$ whenever the mass is not changing.

A 1400 kg car reaching 100 km/h — that is 27.8 m/s — in 8.5 s has an average acceleration of $a = 27.8/8.5 = 3.27$ m/s², so the net force driving it forward is $F = 1400 \times 3.27 \approx 4580$ N. The engine has to supply more than that, because drag and rolling resistance are pulling the other way and the 4580 N is what is left over after they have taken their share.

Almost every other force relation on this site is this one wearing a hat. Weight is $F = ma$ with $a = g$. Centripetal force is $F = ma$ with $a = v^2/r$. Impulse is this law integrated over time, and the work–energy theorem is it integrated over distance. Its rotational twin, $\tau = I\alpha$, swaps torque for force and moment of inertia for mass and behaves identically.

The word doing the most work in the law is "net", and it is the word most often dropped. A crate being pushed with 200 N across a floor that resists with 150 N of friction accelerates as though 50 N were acting, not 200. If an object moves at constant speed the net force on it is zero, however many forces are actually pushing on it. The second mistake is arithmetically worse: kilograms are not a force. A "70 kg load" is a mass, and the force it exerts on its hanger is $70 \times 9.81 \approx 687$ N. Feeding 70 into this calculator as a force when you meant a mass is wrong by a factor of 9.81. The imperial world hides the same trap behind identical words — the pound-mass and the pound-force are different quantities related by 32.174 ft/s², which is where the notorious $g_c$ conversion factor comes from. Use the unit selectors and let them handle it.