Terminal velocity

Near the surface of the Earth, any object falling freely will have an acceleration of about 9.8 metres per second squared (m/s2). Objects falling through a fluid eventually reach terminal velocity. At terminal velocity, the object moves at a steady speed in a constant direction because the resultant force acting on it is zero. For example, a skydiver falling spread-eagled through the air reaches a maximum speed of about 53 m/s.

Three stages of falling

There are three stages as an object falls through a fluid:

  1. at the start, the object accelerates downwards due to the force of gravity
  2. as the object's speed increases, frictional forces such as air resistance or drag increase
  3. at terminal velocity, the weight of the object due to gravity is balanced by the frictional forces, and the resultant force is zero

The weight of an object does not change as it falls, as long as it stays whole.

A skydiver

The diagram shows what happens to the speed of a skydiver from when they leave the aircraft, to when they reach the ground after their parachute opens.

Rises as skydiver accelerates, levels off as air resistance increases, terminal speed reached, resistance, weight balanced. Canopy opens, drop in speed, air resistance increases, graph returns to 0.

Before the parachute opens:

  1. Immediately on leaving the aircraft, the skydiver accelerates downwards due to the force of gravity. There is no air resistance acting in the upwards direction, and there is a resultant force acting downwards so the skydiver accelerates towards the ground.
  2. As the skydiver gains speed, their weight stays the same but the air resistance increases. There is still a resultant force acting downwards, but this gradually decreases.
  3. Eventually, the skydiver's weight is balanced by the air resistance. There is no resultant force and the skydiver reaches terminal velocity.

When the parachute opens, the air resistance increases. The skydiver slows down until a new, lower terminal velocity is reached.

Note that the skydiver does not go upwards when the parachute opens, even though this can appear to happen when a skydiver is being filmed. The illusion happens because the person with the camera opens their parachute later on, so falls downwards past the skydiver.

Velocity-time graphs for falling objects

The diagram shows a velocity-time graph for an object falling through a fluid, eg air, water, oil.

A velocity/time graph. The line follows a steep gradient and curves round to horizontal.

Between A and B

The object accelerates at first because of the force of gravity. Its speed increases. The resultant force acts downwards because the frictional force acting against it is less than the weight of the object.

Between B and C

The object is still accelerating but its acceleration decreases as time goes by. Its speed still increases but by a smaller amount. The resultant force still acts downwards but is decreasing. This is because the frictional force acting against it is increasing as the speed increases, but is still less than the weight of the object.

Between C and D

The object is not accelerating any more. It has reached its terminal velocity and is falling at a steady speed. The resultant force is zero because the frictional force acting against it is now the same as the weight of the object.

The object does not stop falling once its resultant force is zero, unless it has hit the ground.