F = ma

Why it matters

Same push, empty trolley vs loaded trolley — you already know the answer in your arms. Newton just wrote your groceries down as an equation.

The idea in plain words

The world's most useful equation. Tap the terms.

F = m × a

A 150 g ball arrives at 20 m/s; a fielder stops it in 0.1 s vs 0.5 s. Compare forces.

Pulling the hands back cuts the sting five-fold

• newton: F — NET force — after friends and enemies cancel
• defined here: 1 N — the force giving 1 kg exactly 1 m/s² — the unit's definition
• the derivation: from momentum — F = Δp/Δt = m(v−u)/t — the second law's original form
• the application: impulse trick — longer stopping time → smaller force: cricketer's pulled hands, crumple zones, gym mats
• Δp = 0.15 × 20 = 3 kg·m/s both times
• F = 3/0.1 = 30 N vs F = 3/0.5 = 6 N

Predict first

The same 20 N force acts on 2 kg and then on 10 kg. The accelerations are…

a = F/m. Force buys acceleration, and mass is the price tag.

• 10 m/s² and 2 m/s² — five times the mass, a fifth the acceleration — correct
• equal — same force, same effect
• 10 m/s² and 50 m/s²

What you do

Hit a = 5 m/s² twice: once brute-force on a heavy cart, once gently on a light one.

Check yourself

A net force of 12 N on 4 kg produces a = …

a = F/m = 12/4 = 3 m/s².

Zero net force on a MOVING body means…

F = ma with F = 0 gives a = 0 — the first law tucked inside the second.

Eggs land safely on a cushion but crack on tiles because the cushion…

Same Δp; F = Δp/Δt — grow the Δt, shrink the F. Every airbag agrees.

• 3 m/s² — correct
• 48 m/s²
• 0.33 m/s²
• it keeps its velocity (a = 0) — correct
• it stops
• it speeds up
• stretches the stopping TIME, shrinking the force — correct
• reduces the egg's momentum
• is magic