Drop something and it speeds up — but not forever. As a falling object gets faster, the drag pushing back on it grows, until drag exactly balances the object’s weight. At that point the forces cancel, the acceleration drops to zero, and the object keeps falling at a steady, top speed: its terminal velocity.
📘 What you need to know
In a vacuum the only force on a falling body is its weight, so it accelerates at g forever.
In a real fluid, drag increases as the object speeds up (from the previous note).
By Newton’s second law (F = ma), a growing drag means the resultant force — and so the acceleration — falls.
When drag = weight, the resultant force is zero, acceleration is zero, and the object falls at constant terminal velocity.
On a velocity–time graph, terminal velocity is where the line levels off (gradient → 0).
A heavier object (same shape) reaches a higher terminal velocity, and reaches it faster.
How a falling object reaches terminal velocity
Picture a skydiver the moment they jump. Follow the story in three stages:
Just after jumping: speed is low, so drag is tiny. Weight is much bigger than drag, so there’s a large downward resultant force — they accelerate at nearly g.
Speeding up: as the diver gets faster, drag grows. The resultant force (weight − drag) shrinks, so the acceleration gets smaller and smaller.
Terminal velocity: eventually drag grows until it equals the weight. Now the resultant force is zero, the acceleration is zero, and the diver falls at a constant top speed.
As the diver speeds up, drag (red) grows until it balances the weight (amber). When drag = weight, acceleration is zero — that’s terminal velocity.
At terminal velocity
drag = weight ⟹ resultant force = 0 ⟹ acceleration = 0
Terminal velocity isn’t unique to skydivers — it happens for anything falling through a gas or a liquid: a raindrop, a ball-bearing dropped in oil, a pebble sinking in water. Same idea every time: speed rises until drag matches weight.
The skydiver’s velocity–time graph
The whole story shows up beautifully on a velocity–time graph. Remember from the graphs note that the gradient of a v–t graph is the acceleration — so watch how the slope changes.
At first the line is steep (large acceleration, close to g).
The line gradually curves and flattens as drag grows and acceleration falls.
It levels off at the first terminal velocity (zero gradient = zero acceleration).
When the parachute opens, drag suddenly jumps far above the weight, so the diver decelerates — the line drops.
It settles at a new, much lower terminal velocity, safe for landing.
A skydiver’s full fall: the velocity rises and levels at a high terminal velocity, then drops when the parachute opens and settles at a lower, safer one.
Important: when the parachute opens the diver slows down — they don’t shoot upward. The line on the graph falls because they’re decelerating to a lower terminal velocity, not moving backwards.
What affects terminal velocity?
For two objects of the same size and shape, the difference comes down to weight:
A heavier object has more weight, so drag has to grow larger before it can balance that weight. That means it reaches a higher terminal velocity.
Because its weight is bigger, the drag force also builds up to the balance point faster, so a heavier object reaches terminal velocity sooner.
Worked example
WE 1
Two skydivers joining up — who jumps first?
Skydivers A and B want to link up as they fall. They have the same surface area and volume, but A is heavier than B. If they want to reach terminal velocity at the same time, who should jump first?
Heavier = more weight → drag must grow larger to balance itso A reaches a higher terminal velocity than BA’s bigger weight makes drag reach the balance point fasterso A reaches terminal velocity sooner than BFor them to get there at the same moment, the slower one (B) needs a head startSkydiver B should jump first
💡 Top tips
Terminal velocity = balanced forces. Always link it back to drag = weight and zero resultant force.
Read the v–t graph by its gradient — flattening means the acceleration is dropping towards zero.
A heavier object (same shape) reaches a higher terminal velocity, and gets there faster.
Parachute opening = deceleration, shown by the velocity line falling to a lower level — not the diver rising.
It works in any fluid — gas or liquid — so the same reasoning applies to a ball dropped in oil.
⚠ Common mistakes
Saying the skydiver moves upward when the parachute opens — they only decelerate.
Thinking acceleration is constant during the fall — it decreases as drag grows.
Confusing “zero acceleration” with “zero velocity” — at terminal velocity the diver is still moving fast, just not speeding up.
Forgetting drag depends on speed — that growing drag is the whole reason terminal velocity exists.
Assuming a lighter object always falls slower — without air resistance (in a vacuum) everything falls together.
That wraps up SL Kinematics! You’ve now got the full toolkit: displacement and velocity, acceleration, the equations of motion, motion graphs, projectiles, fluid resistance, and terminal velocity. Next topic builds on all of this — Forces & Momentum.
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