Terminal velocity
Forces in Action - OCR A-Level Physics
Key Definition
Terminal velocity
The constant velocity reached when the drag force on a falling object equals its weight, so the resultant force and acceleration are zero.
The constant velocity reached when the drag force on a falling object equals its weight, so the resultant force and acceleration are zero.
- When the object first starts falling, weight $>$ drag, so the resultant force is downward and the object accelerates.
- As speed increases, drag increases. The resultant force, and therefore the acceleration, decreases.
- Eventually $\text{drag} = \text{weight}$. The resultant force is zero, the acceleration is zero, and the object falls at constant terminal velocity.
- A parachutist reaches terminal velocity twice: about $55 \text{ m s}^{-1}$ in free fallMotion under gravity alone, with no other forces acting., then about $5 \text{ m s}^{-1}$ after the parachute opens.
- Opening the parachute suddenly increases surface area, so drag jumps. The resultant force is now upward, so the parachutist decelerates until drag falls back to equal the weight at a new, lower terminal velocity.
$$\text{At terminal velocity:}\quad F_{\text{drag}} = W = mg$$
Common Mistake
MEDIUM
Students often: say the parachutist "stops" when the parachute opens.
Instead: they decelerate but keep moving downward. The resultant force points up; the velocity still points down. They reach a new, lower terminal velocity, not zero.
Instead: they decelerate but keep moving downward. The resultant force points up; the velocity still points down. They reach a new, lower terminal velocity, not zero.
Examiner Tips and Tricks
- Always link the shape of the $v$-$t$ graph back to the resultant force at each labelled point.
- State "drag equals weight" word-for-word; markers look for that exact phrase at the terminal-velocity stage.
Worked Example [4 marks]
Describe and explain the shape of the velocity-time graph for a parachutist who jumps from a plane and later opens a parachute.
Show Solution
1
Initially, velocity increases rapidly because weight >> drag, giving a large downward resultant force and large accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻².
[1]2
As speed increases, drag increases, so the resultant force decreases and the rate of accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻². decreases (the graph curves, becoming less steep)
[1]3
Terminal velocity is reached when $F_{\text{drag}} = W$; the graph becomes horizontal (constant velocity).
[1]4
When the parachute opens, drag suddenly exceeds weight (increased surface area). The parachutist decelerates to a new, lower terminal velocity where drag once again equals weight
[1]Answer
The graph shows increasing velocity with decreasing gradient, levelling off at terminal velocity, then a sudden decrease when the parachute opens, levelling off again at a lower terminal velocity.