Inertia Β· Objects at rest and constant velocity Β· Terminal velocity Β· Drag and air resistance
AQA GCSE Physics 4.5 Β· Higher Tier
π΅ State Newton's First Law and explain what it means for objects at rest and objects moving at constant velocity.
π£ Define inertia and explain how an object's mass relates to its tendency to resist changes in motion.
π’ Identify and describe drag forces, including air resistance, and explain how they arise.
π‘ Explain the process by which a falling object reaches terminal velocity, with reference to resultant forces.
π΄ Analyse velocityβtime graphs for objects falling under gravity and reaching terminal velocity.
βͺ Apply Newton's First Law to real-world contexts such as skydiving, cycling, and car crashes.
Newton's First Law of Motion
Newton's First Law: An object will remain at rest, or continue to move in a straight line at a constant velocity, unless acted upon by a resultant (net) force.
This law is one of the most profound statements in all of physics. It tells us something that is not obvious from everyday experience: motion does not require a force to maintain it. A force is only needed to change motion β to speed something up, slow it down, or make it change direction.
In everyday life, objects seem to slow down and stop without any obvious push. This is because friction and air resistance are always acting, providing the resultant force that decelerates the object. Remove those forces (in deep space, for example) and an object would travel in a straight line at constant speed forever.
Key idea: If the resultant force on an object is zero, the object is either stationary or moving at constant velocity. Both of these are called equilibrium.
Two situations of zero resultant force:
At rest: A book on a table. Gravity pulls it down; the normal contact force from the table pushes it up. These balance, so the resultant force is zero and the book stays still.
Constant velocity: A car cruising on a motorway at 70 mph. The driving force from the engine equals the total drag and friction forces. Resultant force = 0, so velocity is constant (same speed, same direction).
Remember: constant velocity means both constant speed and constant direction. An object moving in a circle at steady speed is NOT at constant velocity because its direction keeps changing β it must have a resultant centripetal force acting on it.
Inertia
Inertia: The tendency of an object to resist any change in its state of rest or uniform motion. It is a property of all matter with mass.
Inertia is directly linked to mass. The greater the mass of an object, the greater its inertia, and the harder it is to change its velocity. This is why it takes much more force to accelerate a lorry from rest than a bicycle, and why a bowling ball is much harder to stop than a tennis ball moving at the same speed.
Inertia β mass (m) | Units: kilograms (kg)
Object
Mass (kg)
Relative Inertia
Tennis ball
0.057
Very low
Adult person
~70
Moderate
Family car
~1500
High
Lorry
~20 000
Very high
Inertia has real safety implications. In a car crash, passengers continue moving forward at the car's original speed (Newton's First Law) even when the car suddenly decelerates. Seatbelts apply a force to change the passenger's velocity along with the car, preventing them from hitting the windscreen. Crumple zones increase the time over which the velocity changes, reducing the force experienced.
Inertial mass is defined as the ratio of force to acceleration: m = F Γ· a. It is a measure of how difficult it is to accelerate an object.
Drag Forces and Air Resistance
Drag: A resistive force that opposes the motion of an object moving through a fluid (liquid or gas). Air resistance is drag in air.
When an object moves through a fluid, the fluid particles must be pushed out of the way. This creates a resistive force in the direction opposite to the object's motion. Drag is not a simple constant β it depends on several factors:
Speed: Drag increases as speed increases. In fact, for many objects drag is approximately proportional to the square of speed (double the speed β roughly four times the drag). This is why it takes disproportionately more fuel to drive at 80 mph than 60 mph.
Cross-sectional area: A larger frontal area creates more drag. A lorry experiences far more air resistance than a sports car at the same speed.
Shape (streamlining): A streamlined, aerodynamic shape allows fluid to flow smoothly around it, reducing drag. Fish, birds, aircraft, and racing cars all have streamlined shapes for this reason.
Fluid density: Drag is greater in denser fluids. Swimming through water requires much more force than running through air at the same speed.
Drag force (F_d) β vΒ² Γ A | where v = speed, A = cross-sectional area
Engineers use drag to their advantage in parachutes and braking systems, but work hard to minimise it in vehicles and aircraft. A parachutist deploys a parachute to increase drag, increasing the resultant upward force and slowing their descent to a safe landing speed.
At low speeds, drag may be small enough to ignore. At high speeds, drag can equal or exceed the driving force, preventing further acceleration.
Terminal Velocity
Terminal velocity: The maximum, constant velocity reached by a falling object when the drag force equals the gravitational force (weight), so the resultant force is zero.
When an object is released from rest and falls through a fluid (such as air), a fascinating sequence of events unfolds:
Initial fall: The object accelerates downward under gravity (weight acts downward). At first, drag is very small because the speed is low. The resultant force is large, so acceleration is approximately g (β 9.8 m/sΒ²) downward.
Increasing drag: As the object speeds up, drag increases. The resultant force (weight β drag) decreases, so the acceleration decreases. The object is still speeding up, but more slowly.
Terminal velocity reached: Eventually, drag equals weight. Resultant force = 0. By Newton's First Law, the object continues at constant velocity β this is the terminal velocity. Acceleration is now zero.
At terminal velocity: Weight = Drag βΉ mg = F_drag
For a skydiver in a belly-to-earth position, terminal velocity is approximately 55β60 m/s (~200 km/h). When the parachute opens, the greatly increased drag means drag now exceeds weight momentarily β the resultant force is now upward β and the skydiver decelerates rapidly to a new, much lower terminal velocity of about 5β6 m/s, safe enough to land.
The terminal velocity of an object depends on its weight and its drag characteristics. A heavier object of the same shape and size will have a higher terminal velocity than a lighter one.
Reading a velocityβtime graph for terminal velocity:
Steep positive gradient at start β large acceleration (small drag)
Zero gradient (horizontal line) β terminal velocity (drag = weight)
If parachute opens: steep negative gradient (deceleration) β new, lower horizontal line (new terminal velocity)
Applying Newton's First Law: Force Diagrams
Newton's First Law connects directly to free body diagrams. For any object, you must identify ALL forces acting on it and find the resultant (vector sum). If the resultant is zero, Newton's First Law tells you the object must be in equilibrium.
Situation
Forces
Resultant
Motion
Book on table
Weight β, Normal β (equal)
Zero
At rest
Skydiver at terminal v
Weight β, Drag β (equal)
Zero
Constant velocity β
Car accelerating
Drive > Drag
Forward
Speeding up
Car braking
Drag + Friction > Drive
Backward
Slowing down
Object in space
None
Zero
Constant velocity (forever)
Always check: is the resultant force zero? If yes β Newton's First Law applies β no change in motion. If no β there will be acceleration (Newton's Second Law: F = ma).
The connection between Newton's First and Second Laws is seamless. When F_net = 0, then a = F/m = 0, confirming constant velocity. Newton's First Law is actually a special case of Newton's Second Law where the resultant force is zero.
Example 1: A skydiver of mass 75 kg jumps from a plane and reaches terminal velocity. Calculate the drag force acting on the skydiver at terminal velocity. (g = 9.8 m/sΒ²)
1Identify what terminal velocity means: At terminal velocity, the resultant force on the skydiver is zero. This means the upward drag force exactly equals the downward weight.
2Calculate the weight of the skydiver:
Weight = mass Γ gravitational field strength
W = m Γ g = 75 Γ 9.8 = 735 N (downward)
3Apply Newton's First Law at terminal velocity:
Resultant force = 0
Drag β Weight = 0
Drag = Weight = 735 N (upward)
β The drag force at terminal velocity = 735 N (acting upward, opposing motion)
Example 2: A car of mass 1200 kg travels at a constant speed along a motorway. The engine exerts a driving force of 800 N. Explain why the car travels at constant speed and calculate the total resistive force acting on it.
1Apply Newton's First Law: The car moves at constant velocity (constant speed in a straight line). By Newton's First Law, the resultant force must be zero.
2Identify the forces acting horizontally:
β Driving force (engine) = 800 N (forward)
β Total resistive force = friction + air resistance (backward)
3Calculate the resistive force:
Since resultant force = 0:
Driving force = Total resistive force
Total resistive force = 800 N
4Explain: The car travels at constant speed because the driving force from the engine is exactly equal and opposite to the total resistive forces (air resistance + friction). The resultant force is zero, so by Newton's First Law there is no acceleration β the velocity stays constant.
β Total resistive force = 800 N (backward). The car is in equilibrium β resultant force = 0 β so it travels at constant velocity.
Example 3: A ball bearing of mass 0.020 kg is dropped into a cylinder of oil. Describe and explain the motion of the ball bearing from the moment it is released until it reaches terminal velocity. Use the concept of resultant force throughout.
1At the instant of release (v = 0):
Weight = mg = 0.020 Γ 9.8 = 0.196 N (downward)
Drag = 0 N (no motion yet)
Resultant force = 0.196 N downward
β The ball bearing accelerates downward at approximately g = 9.8 m/sΒ²
2As speed increases:
Drag increases with speed (drag β vΒ²).
Resultant force = Weight β Drag = 0.196 β F_drag
This resultant force decreases as drag grows.
β The ball bearing continues to accelerate, but with decreasing acceleration.
3At terminal velocity:
Drag has grown until: Drag = Weight = 0.196 N
Resultant force = 0
By Newton's First Law β constant velocity (terminal velocity)
Acceleration = 0
4Summary of motion:
Phase 1: Large downward resultant force β rapid acceleration
Phase 2: Decreasing resultant force β decreasing acceleration (still speeding up)
Phase 3: Zero resultant force β constant terminal velocity
β The ball bearing accelerates from rest with decreasing acceleration as drag grows, until drag equals weight (0.196 N). At this point the resultant force is zero and the ball bearing moves at constant terminal velocity.
Example 4: A skydiver of mass 80 kg is falling at terminal velocity of 56 m/s. She then opens her parachute, increasing her cross-sectional area significantly. The drag force immediately after opening is 1800 N. Calculate the resultant force and the initial acceleration at this moment. (g = 9.8 m/sΒ²)
1Calculate the weight:
W = mg = 80 Γ 9.8 = 784 N (downward)
2Identify the forces immediately after the parachute opens:
Drag = 1800 N (upward)
Weight = 784 N (downward)
Drag > Weight β resultant force is upward
3Calculate the resultant force:
F_resultant = Drag β Weight = 1800 β 784 = 1016 N upward
4Calculate the acceleration using F = ma:
a = F Γ· m = 1016 Γ· 80 = 12.7 m/sΒ²
Direction: upward (i.e., a deceleration since she is moving downward)
The skydiver decelerates rapidly, slowing to a new, much lower terminal velocity.
β Resultant force = 1016 N upward. Initial deceleration = 12.7 m/sΒ² (upward, opposing downward motion β she rapidly slows down).
Question 1: A car travels at constant velocity along a straight, level road. Which of the following statements is correct?
Question 2: Which of the following correctly describes what happens to the drag force on a falling object as its speed increases?
Question 3: A cyclist of mass 70 kg (including bicycle) reaches terminal velocity on a flat road. The total drag and friction force is 150 N. What is the driving force the cyclist must produce? Give your answer in newtons.
Question 4: A skydiver of mass 65 kg falls at terminal velocity. What is the drag force acting on them? (g = 9.8 m/sΒ²) Give your answer in newtons.
Question 5: Which of the following factors does NOT increase the drag force on a moving object?
Challenge 1 (6 marks): A parachutist of mass 90 kg jumps from an aircraft and falls vertically. The table below shows data from their fall.
Time (s)
Velocity (m/s)
0
0
5
40
10
52
15
56
20
56
(a) Explain why the acceleration decreases between 0 s and 15 s. (b) Calculate the weight of the parachutist. (g = 9.8 m/sΒ²) (c) State the size of the drag force at t = 20 s and explain your reasoning. (d) Calculate the acceleration at t = 5 s using the data in the table.
(a) As the parachutist speeds up, the drag force increases (drag β vΒ²). The resultant force = Weight β Drag decreases as drag grows, so the acceleration decreases. [2 marks]
(b) W = mg = 90 Γ 9.8 = 882 N [1 mark]
(c) At t = 20 s, velocity is constant (56 m/s), so the resultant force = 0. Therefore drag = weight = 882 N upward. [1 mark]
(d) Using the gradient between t = 0 and t = 5 s (where acceleration is changing, so this is an approximation):
a = Ξv Γ· Ξt = (40 β 0) Γ· (5 β 0) = 8.0 m/sΒ² [2 marks]
(Note: this is less than g = 9.8 m/sΒ² because drag is already acting at this point.)
Challenge 2 (5 marks): A cyclist is travelling at terminal velocity of 12 m/s on a flat road. The total resistive force (air resistance + friction) is 95 N. The cyclist then doubles their speed to 24 m/s by going downhill, and air resistance becomes the dominant force, increasing by a factor of 4 (as expected for doubled speed).
(a) State the driving force the cyclist exerts at 12 m/s on the flat. (b) At 24 m/s, if friction remains 15 N and air resistance has increased by a factor of 4 from its value at 12 m/s, calculate the total drag force at 24 m/s. (c) Explain what happens to the cyclist's motion if they maintain the same pedalling force as at 12 m/s while travelling at 24 m/s.
(a) At terminal velocity, driving force = resistive force = 95 N [1 mark]
(b) Air resistance at 12 m/s = 95 β 15 = 80 N
Air resistance at 24 m/s = 80 Γ 4 = 320 N
Total drag at 24 m/s = 320 + 15 = 335 N [2 marks]
(c) Driving force maintained = 95 N. Total drag = 335 N.
Resultant force = 95 β 335 = β240 N (backward/opposing motion).
The resultant force is opposite to the direction of motion, so the cyclist decelerates. They will slow down from 24 m/s until a new equilibrium is reached where drag again equals the driving force. [2 marks]
Challenge 3 (6 marks β extended writing): A student claims: "Once an object is moving, you need to keep applying a force to keep it moving, otherwise it will always slow down and stop." Evaluate this claim with reference to Newton's First Law, inertia, and the role of friction and drag. Use examples to support your answer.
Model answer (6 marks):
The student's claim is incorrect in principle, but reflects everyday experience on Earth.
Newton's First Law states that an object will continue to move at constant velocity unless a resultant force acts on it. No force is needed to maintain constant motion β force is only needed to change motion. This is the property of matter called inertia: objects resist changes to their state of motion. [2 marks]
On Earth, objects appear to slow down because friction and drag (air resistance) always act on moving objects, providing a resultant force opposing the motion. This is why a ball rolled along the floor stops β it is friction from the floor and air resistance that decelerate it, not the absence of a driving force. [2 marks]
In an environment where friction and drag are removed β for example, a spacecraft in deep space β an object would continue moving in a straight line at constant velocity indefinitely without any force being applied. The Voyager probes, launched in 1977, have been travelling through space with no propulsion for decades, demonstrating this principle. Similarly, a puck on a frictionless air hockey table barely decelerates because the surface removes friction. [2 marks]
Therefore, the student is confusing the effect of resistive forces (which are always present on Earth) with the need for a continuing force to maintain motion. A force is only needed to overcome resistance, not to sustain motion itself.
Challenge 4 (4 marks): Two identical balls, A and B, are dropped from the same height. Ball A falls through air; Ball B falls through oil (which is much denser than air). Both eventually reach terminal velocity.
(a) Which ball reaches terminal velocity first? Explain why. (b) Which ball has the higher terminal velocity? Explain in terms of forces.
(a)Ball B (in oil) reaches terminal velocity first.
Oil is much denser than air, so it exerts a much greater drag force at any given speed. Ball B therefore experiences a large drag force even at low speeds, and drag rapidly grows to equal the ball's weight. Ball B reaches terminal velocity after falling only a very short distance, whereas Ball A (in air) must speed up to a much higher velocity before drag equals its weight. [2 marks]
(b)Ball A (in air) has the higher terminal velocity.
At terminal velocity, drag = weight for both balls. Since weight is the same for both balls, the drag at terminal velocity must also be equal. However, since air produces much less drag per unit speed than oil, Ball A must reach a much higher speed before the drag force equals its weight. Ball B requires only a low speed in the denser oil to generate the same drag force. [2 marks]