Section 1 of 6Tools you need
| Equation | Symbols and units |
|---|---|
| F = m × a | force F (N), mass m (kg), acceleration a (m/s2) |
| v2 − u2 = 2 × a × s | final speed v and initial speed u (m/s), acceleration a (m/s2), distance s (m) |
| work done = F × d | work (J), force (N), distance (m) |
| Ek = ½ × m × v2 | kinetic energy (J), mass (kg), speed (m/s) |
Section 2 of 6Worked estimate
1
A car of mass 1200 kg is travelling at 20 m/s and stops in a braking distance of 40 m.
2
Use v2 − u2 = 2as: 0 − 400 = 2 × a × 40, so a = −5 m/s2. The negative sign shows deceleration.
3
Apply F = m × a: F = 1200 × 5 = 6000 N.
4
Check with energy: Ek = ½ × 1200 × 202 = 240 000 J, and 240 000 ÷ 40 = 6000 N. Both methods agree.
Section 3 of 6Making sensible estimates
Typical masses
- Typical masses A small car is about 1000 kg, a family car 1500 kg, and a loaded lorry can be 30 000 kg.
Typical speeds
- Typical speeds 30 mph is about 13 m/s; 60 mph is about 27 m/s; 70 mph is about 31 m/s.
Typical decelerations
- Typical decelerations Normal braking is a few m/s2.
- An emergency stop on a dry road might reach about 8 to 10 m/s2.
Section 4 of 6Is the force safe?
Size of the braking force
Too small
- Too small The car takes too far to stop and may hit the hazard.
Too large
- Too large Large deceleration can cause injury to passengers and can make the tyres lose grip and skid.
Effect of speed
- Effect of speed At twice the speed, stopping within the same distance needs four times the braking force.
Effect of mass
- Effect of mass A vehicle with twice the mass needs twice the force to achieve the same deceleration.
Section 5 of 6Key terms
| Term | Meaning |
|---|---|
| Deceleration | A negative acceleration, the rate at which speed decreases. |
| Braking force | The resultant force that slows a vehicle down. |
| Estimate | An approximate value found using sensible, rounded numbers. |
| Work done | Energy transferred when a force moves an object through a distance. |
| Kinetic energy | Energy stored in a moving object because of its mass and speed. |
Section 6 of 6Exam technique
1
Using speeds in mph or km/h in equations. Convert to m/s first.
2
Forgetting to square the speed in the kinetic energy equation.
3
Leaving out the negative sign for deceleration in the calculation, then confusing what the answer means.
4
Quoting force with no unit, or giving 6000 N as 6000 kg.