Every day people and vehicles travel at different speeds and are exposed to large accelerations and forces.

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 approximate. The table gives some examples.

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

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

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

It takes a cyclist approximately 12 s to reach a top velocity of 7.5 m/s. To estimate the cyclist's acceleration, use the formula:

Force can be estimated using the equation:

force = mass × acceleration

This is when:

- force is measured in newtons (N)
- mass is measured in kilograms (kg)
- acceleration is measured in metres per second squared (m/s
^{2})

For example, to estimate the force needed to accelerate a family car to its top speed on a single carriageway, use the approximate values given above of ~1,600 kg for the mass of the car and ~3 m/s^{2} for the acceleration.

Force = 1,600 × 3

Force = ~4,800 N

- Question
Estimate the force needed to accelerate a lorry to its top speed on a single carriageway, using the values given above.

Force (N) = mass (kg) × acceleration (m/s

^{2})Force = 36,000 × 0.4

Force = ~14,400 N