Intermediate · 12 min
Modelling stopping distance
Separate reaction distance from braking distance in a simplified motion model.
Two stages of a stop
In a simple model, an object continues at its initial speed during a response interval and then slows under a braking force. Distance during the response interval is speed multiplied by time. Total stopping distance includes both this distance and the braking distance. Keep the model's assumptions explicit: the speed is constant in the first stage and the deceleration is constant in the second.
Worked example
A model vehicle moves at 10 m/s during a 0.6 s response interval. Distance before braking = 10 × 0.6 = 6 m
Braking distance depends on speed squared
For constant deceleration magnitude b, with initial speed u and final speed zero, braking distance is d = u² ÷ (2b). At the same b, doubling initial speed makes this distance four times greater. Real response times and braking forces vary with conditions, so these exercises are idealised calculations, not stopping-distance predictions for a real journey.
Worked example
For u = 10 m/s and b = 5 m/s²: Braking distance = 10² ÷ (2 × 5) = 10 m With a 6 m response distance, total stopping distance is 16 m.
Compare a model at two speeds
- With response time 1 s and constant deceleration magnitude 4 m/s², calculate the total model stopping distance at 8 m/s.
- Repeat at 16 m/s. Compare how the response and braking distances scale separately.