سائنس
Terminal Velocity: When Drag Catches Up With Weight
Terminal velocity is where drag has grown equal to weight, so the resultant force is zero. Traced through a skydiver graph, parachute plateau included.
Terminal velocity
Terminal velocity is the constant speed reached by a falling object once the upward drag force acting on it has become equal in size to its downward weight.
- طلبہ کہاں پڑھتے ہیں
- Grade 9 science, and again at GCSE and IGCSE physics, where describing the skydiver's velocity–time graph is a standard extended-response question.
مختصر جواب
Terminal velocity is the steady speed a falling object reaches when the drag pushing up on it has grown equal to the weight pulling it down. The resultant force is then zero, so the acceleration is zero and the speed stops changing. It is a constant velocity, not a fastest possible one.
ایک مثال
weight 700 N downwards, drag 700 N upwards → resultant 0 N → acceleration 0 m/s²
Nothing has stopped pulling the skydiver down; gravity is acting exactly as strongly as it was at the moment of the jump. What has changed is that the air is now pushing back just as hard. Two equal and opposite forces leave a resultant of zero, and by Newton's first law an object with no resultant force on it keeps moving at a constant velocity — which here means continuing to fall, quickly, but no longer any quicker.
One force is constant, the other is not
The skydiver's weight does not change during the fall. Their mass is the same and gravitational field strength is effectively the same, so the downward force stays put at whatever it was on the ground. Everything that happens comes from the other force.
Drag depends on speed. At the instant of jumping the speed is zero, so the drag is zero, so the resultant is the full weight and the acceleration is at its greatest — close to 9.8 m/s². As the speed builds, the drag builds with it, the resultant shrinks, and the acceleration falls. The diver is still speeding up, but by less in each successive second, which is exactly what a curve of decreasing gradient looks like.
Five stages of the velocity–time graph
The graph is worth learning as a shape rather than as a set of words, because every part of it is explained by the balance of the same two forces. Textbook figures put a belly-down skydiver's terminal velocity at roughly 50 m/s, and the plateau after the parachute opens at a small fraction of that.
Note where the second stage differs from the fourth. Between opening the parachute and reaching the new plateau the diver is slowing down while still falling — the graph slopes downwards, but it stays above the axis the whole time.
- Steep, almost straight start — drag is negligible, so acceleration is about 9.8 m/s²
- Curve flattening — drag grows with speed, resultant force shrinks, acceleration falls
- First plateau — drag equals weight, resultant zero, constant terminal velocity
- Sharp fall in the line — the parachute opens, area increases, drag now exceeds weight, so the resultant force acts upwards and the diver decelerates
- Second, much lower plateau — drag and weight balance again, at a new and far slower terminal velocity
Three things terminal velocity is not
It is not a universal speed limit for falling. Change the shape and you change the number: the same person diving head-first, with far less area facing the air, reaches a considerably higher terminal velocity than they do spread flat, with no change in weight at all.
Nor is it caused by gravity weakening or running out. And it does not exist where there is no atmosphere. On the Moon there is no air to provide drag, so nothing ever reaches a terminal velocity — which is why the hammer and feather dropped there during Apollo 15 hit the ground together.
عام سوالات
Does a heavier object have a higher terminal velocity?
Yes, if the shape and size are the same. More weight needs more drag to balance it, and more drag requires more speed, so the balance point moves higher up. This is why a marble falls faster than a beach ball, even though the beach ball is much larger.
Is the skydiver still accelerating at terminal velocity?
No. The resultant force is zero, so the acceleration is zero. This is the sentence to write in an exam answer, because saying that the diver has stopped speeding up describes the graph while explaining nothing. The forces are balanced; that is the reason, and the constant speed is the consequence.
Why does the graph curve instead of rising in a straight line?
Because the acceleration is not constant. A straight line would mean the velocity gains the same amount every second, which would require an unchanging resultant force. Drag grows as the speed grows, so the resultant force shrinks continuously and each second adds a little less speed than the one before.
Does terminal velocity happen in water?
Yes, and much sooner. Water is far denser than air, so drag builds very quickly, and a stone dropped into a deep pool reaches a steady sinking speed after a short distance. Upthrust joins the calculation there too, acting upwards alongside the drag.
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