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Mechanics formulas

Newton's second law

Calculate net force, mass, or acceleration using the relationship between force and motion.

Formula

F=m×a F = m × a

The net external force on a system equals its mass multiplied by its acceleration.

Newton's second law calculator

What do you want to calculate?

Known values

The result updates automatically.

Result

20 N

Substitution and calculation

F = m × a = 10 kg × 2 m/s² = 20 N

Symbols and units

SymbolQuantitySISupported units
Fnet forceVector sum of the external forces along the selected axis.NN, kN
mmassInertial mass of the system.kgkg, g
aaccelerationAcceleration component in the direction of the net force.m/s²m/s², km/h/s, km/h²

Formula rearrangements

Calculate net force

F = m × a

Calculate mass

m = F / a

Calculate acceleration

a = F / m

Worked examples

Net force accelerating a car

A 1200 kg car accelerates at 2.5 m/s². Find the net force.

  1. 1Step 1: Use F = m × a.
  2. 2Step 2: Substitute m = 1200 kg and a = 2.5 m/s².
  3. 3Step 3: Multiply to obtain 3000 N, or 3 kN.

Result: 3,000 N (3 kN)

Mass from force and acceleration

A net force of 600 N produces an acceleration of 3 m/s². Find the mass.

  1. 1Step 1: Use m = F / a.
  2. 2Step 2: Substitute F = 600 N and a = 3 m/s².
  3. 3Step 3: Divide 600 by 3 to obtain 200 kg.

Result: 200 kg

Sources and review