Stopping distances, work, power and Hooke's law
Stopping distance
Stopping distance = thinking distance + braking distance.
| Component | Affected by |
|---|---|
| Thinking distance | Reaction time: tiredness, alcohol, drugs, distractions |
| Braking distance | Speed (squared!), road condition (wet/icy), tyre tread, brake condition, mass of vehicle |
Doubling the speed quadruples the braking distance because the kinetic energy (and so the work the brakes must do) goes up with v^2.
Work done
Work = force x distance moved in the direction of the force.
W = F x d (joules).
Energy is transferred to the object — kinetic, gravitational, elastic, thermal, etc.
Power
Power = energy transferred per second = work done per second.
P = E / t = W / t (watts).
Hooke's law
For a spring (within its elastic limit):
F = k x e,
where F is the force in newtons, k is the spring constant in N/m, and e is the extension in metres.
A force-extension graph is a straight line through the origin while the spring obeys Hooke's law; it curves above the limit of proportionality and the spring may not return to its original length above the elastic limit.
Elastic potential energy
When a spring is stretched (or compressed) it stores elastic PE.
E_p = 1/2 x k x e^2.
This is the area under a force-extension graph in the linear region.
✦Worked example
A 4 N force stretches a spring by 0.05 m within its elastic limit.
(a) Spring constant: k = F/e = 4/0.05 = 80 N/m. (b) Elastic PE: E_p = 1/2 x 80 x 0.05^2 = 1/2 x 80 x 0.0025 = 0.10 J.
WJEC exam tip
For braking-distance questions, "speed doubles -> braking distance quadruples" is the headline phrase. Always link it to the kinetic energy 1/2 m v^2 — examiners reward the physics, not just the numerical fact.
AI-generated · claude-opus-4-7 · v3-wjec-combined-science-leaves