Estimating acceleration
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 |
Vehicle | Family car |
---|---|
Maximum legal speed on a single carriageway (m/s) | ~27 |
Mass (kg) | ~1,600 |
Acceleration (m/s²) | ~3 |
Vehicle | Lorry |
---|---|
Maximum legal speed on a single carriageway (m/s) | ~22 |
Mass (kg) | ~36,000 |
Acceleration (m/s²) | ~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