Terminal Velocity and Stopping Distance

Terminal velocity — the constant velocity reached by a falling object when the drag force acting upwards has grown equal to its weight, so the resultant force is zero.

The sequence matters, and questions ask for it in order:

1. At release the only force is weight, so the object accelerates downwards at about 10 m/s².
2. As it speeds up, air resistance increases, because drag grows with speed.
3. The resultant force falls, so the acceleration decreases — it is still speeding up, but less rapidly.
4. When drag equals weight the resultant is zero, the acceleration is zero, and the object falls at a steady terminal velocity.

Notice that the object never slows down in this sequence unless something changes. A parachute opening increases drag sharply, so drag briefly exceeds weight, the resultant acts upwards, and the skydiver decelerates to a new, lower terminal velocity.

On a velocity–time graph terminal velocity is where the curve flattens to a horizontal line.

Stopping distance is the total distance from spotting a hazard to standing still:

stopping distance = thinking distance + braking distance

Thinking distance — how far the vehicle travels during the driver's reaction time, before the brakes are touched. It increases with speed, and with anything that lengthens reaction time: tiredness, alcohol, drugs, distraction.

Braking distance — how far it travels once the brakes are applied. It increases with speed, and with anything that reduces the braking force or increases the mass: wet or icy roads, worn tyres, worn brakes, a heavily loaded vehicle.

The distinction examiners look for: a tired driver has a longer thinking distance but an unchanged braking distance. An icy road lengthens the braking distance but not the thinking distance. Sorting a given factor into the right one of the two is where the marks are.

Example: doubling the speed roughly doubles the thinking distance, because it is simply speed × reaction time. The braking distance goes up by about four times, because the kinetic energy to be removed depends on v². This is why speed limits matter more than they look.