Newton's Second Law — F = ma

Newton's second law says the acceleration is the force divided by the mass: a = F/m. Double the force on the same body and it accelerates twice as fast. Double the mass under the same force and it accelerates half as fast. That is the whole law, and the race here shows the second half of it — both trolleys get an identical push, but the heavier one falls steadily behind because every kilogram of mass resists being accelerated.

The unit follows directly from the equation. One newton is the force that gives one kilogram an acceleration of one metre per second squared, so 1 N = 1 kg·m/s². It also explains weight: weight is simply the force gravity exerts on a mass, W = mg, which is why a 10 kg component weighs about 98 N.

Note what happens when the force reaches zero: the trolley does not stop, it keeps whatever speed it already had. That is Newton's first law, and the second law contains it — no force means no acceleration, not no motion. Only a resisting force such as friction or drag would slow it down.

• Try this: Hold the mass and double the force. What happens to the acceleration, and to the gap between the two trolleys?
• Try this: Hold the force and double the mass. Why does the acceleration halve rather than the speed?
• Try this: Set the force to zero while the trolleys are moving. Do they stop? Why not?