Newton's laws of motion help explain why an object needs a force to make it move - inertia also explains this. Momentum, on the other hand, explains some of the most important interactions in nature.

Newton's second law of motion can be described by this equation:

- resultant force = mass × acceleration
- F = m a

This is when:

- resultant force (F) is measured in newtons (N)
- mass (m) is measured in kilograms (kg)
- acceleration (a) is measured in metres per second squared (m/s²)

The equation shows that the acceleration of an object is:

- proportional to the resultant force on the object
- inversely proportional to the mass of the object

In other words, the acceleration of an object increases if the resultant force on it increases, and decreases if the mass of the object increases.

Newton's second law can either be expressed as "resultant force = mass × acceleration" or "The acceleration of an object is directly proportional to the resultant (or net) force, in the same direction as the force, and inversely proportional to the mass of the object."

The ratio of force over acceleration is the definition of inertial mass. Inertial mass is a measure of how difficult it is to change the velocity of an object. It is defined as 'the ratio of force over acceleration'. Objects with a greater mass have greater inertia and so a greater resultant force will be required to cause the same acceleration.

Calculate the force needed to accelerate a 22 kg cheetah at 15 m/s².

- Question
Calculate the force needed to accelerate a 15 kg gazelle at 10 m/s².

It is important to be able to estimate speeds, accelerations and forces involved in road vehicles. The symbol ~ is used to indicate that a value or answer is an approximate one. The table gives some examples.

Vehicle | Maximum legal speed on a single carriageway in m/s | Mass in kg | Acceleration in m/s2 |
---|---|---|---|

Family car | ~27 | ~1,600 | ~3 |

Lorry | ~22 | ~36,000 | ~0.4 |

Estimate the force needed to accelerate a family car to its top speed on a single carriageway.
Using values of ~1,600 kg and ~3 m/s^{2}, and F = m a:

- Question
Estimate the force needed to accelerate a lorry to its top speed on a single carriageway.

Using values of ~36,000 kg and ~0.4 m/s

^{2}, and F = m a: