Making estimations

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.

VehicleMaximum 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

Estimating acceleration

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:

acceleration~(m/s^2) = \frac{change~in~velocity~(m/s)}{time~taken~(s)}

acceleration = 7.5 \div 12

acceleration = 0.6~m/s^2~(2sf)

Estimating force - Higher

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/s2)

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/s2 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/s2)

Force = 36,000 × 0.4

Force = ~14,400 N