Terminal Velocity
- For a body in free fall, the only force acting is its weight and its acceleration g is only due to gravity.
- The drag force increases as the body accelerates
- This increase in velocity means the drag force also increases
- Due to Newton’s Second Law, this means the resultant force and therefore acceleration decreases (recall F = ma)
- When the drag force is equal to the gravitational pull on the body, the body will no longer accelerate and will fall at a constant velocity
- This the maximum velocity that the object can have and is called the terminal velocity
A skydiver in freefall reaching terminal velocity
- The graph shows how the velocity of the skydiver varies with time
- Since the acceleration is equal to the gradient of a velocity-time graph, the acceleration decreases and eventually becomes zero when terminal velocity is reached
Worked example
Skydivers jump out of a plane at intervals of a few seconds.
Skydivers A and B want to join up as they fall.
If A is heavier than B, who should jump first?
- Skydiver B should jump first since he will take less time to reach terminal velocity
- His terminal velocity will also be a lower speed than that of skydiver A
- This is because skydiver A has a higher mass, and hence, weight
- A greater weight means a greater acceleration for A than B at every stage until terminal velocity
- Air resistance gets larger with speed, so for air resistance to match A's weight, A must be travelling faster than B at terminal velocity
- This means if A were to jump first, skydiver B would never catch up
- Skydiver B must jump first, then skydiver A can catch up
Examiner Tip
- Exam questions about terminal velocity tend to involve the motion of skydivers as they fall
- A common misconception is that skydivers move upwards when their parachutes are deployed - however, this is not the case, they are in fact decelerating to a lower terminal velocity
- What do you think this would look like on the graph above?
