Impulse is the effect of a force acting over a time interval. For a constant force, or when an average force is known, it is calculated as impulse = force × time. More fundamentally, the net impulse on an object equals its change in momentum.
J = F_avg Δt = Δp = p_f - p_i
This relationship is the impulse-momentum theorem. It explains why a brief, large collision force and a smaller force acting for longer can produce the same change in motion. For IB Physics students, understanding impulse means connecting forces, momentum, vector direction, force-time graphs, and collision safety rather than simply memorizing a formula.
What is impulse in physics?
Impulse measures the total effect of a force over the time for which it acts. Its usual symbol is J, although you should always follow the notation given in a question.
For a constant resultant force:
J = F_net Δt
where:
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J is impulse
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F_net is the resultant or net force
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Δt is the time interval during which the force acts
The word resultant matters. If several forces act on an object, the impulse responsible for its overall momentum change comes from their vector sum, not automatically from one selected force.
For example, a resultant force of 50 N acting to the right for 0.20 s produces an impulse of:
J = 50 × 0.20 = 10 N s to the right
A force of 100 N acting for 0.10 s would produce the same impulse. The forces are different, but the product of force and time is equal.
Impulse is a vector quantity. It therefore has both magnitude and direction, with the direction determined by the net force and the resulting change in momentum.
How impulse connects to momentum
Linear momentum is defined as:
p = mv
where m is mass and v is velocity. Momentum is also a vector because velocity has direction.
Newton's second law can be expressed in its momentum form as:
F_net = Δp / Δt
Rearranging gives:
F_net Δt = Δp
Since the left side is impulse:
J = Δp
This is the impulse-momentum theorem. It states that the net impulse acting on an object equals its change in momentum.
For an object of constant mass:
J = m(v_f - v_i)
The expression mΔv is appropriate when mass remains constant. The more general expression is Δp = p_f - p_i, which should be used when mass changes or when the initial and final momenta must be considered separately.
Students reviewing the wider syllabus context can use the IB Physics A.2 Forces and Momentum topic hub. This article focuses specifically on impulse rather than duplicating the topic-wide treatment of forces, momentum conservation, collisions, and explosions.
Impulse, momentum, force, and energy compared
These quantities are related, but they are not interchangeable.
QuantityMeaningCommon equationSI unitScalar or vector?ForceRate at which momentum changesF = Δp/ΔtNVectorImpulseEffect of force over timeJ = F_avg ΔtN sVectorMomentumMass multiplied by velocityp = mvkg m s⁻¹VectorKinetic energyEnergy associated with motionE_k = ½mv²JScalar
Impulse and momentum have equivalent units:
1 N s = 1 kg m s⁻¹
This follows because 1 N = 1 kg m s⁻². Multiplying by seconds produces kg m s⁻¹, the unit of momentum.
Do not confuse impulse, whose unit may be written N s, with energy, whose unit is the joule J. The symbol J can represent impulse in an equation, while an upright J after a numerical value represents joules. Context and units distinguish them.
Why impulse is a vector
The sign of an impulse communicates direction. Before calculating, choose a positive direction and assign signs consistently to every velocity, momentum, force, and impulse.
Suppose a 0.15 kg ball moves to the right at 20 m s⁻¹, rebounds, and then travels to the left at 12 m s⁻¹. Taking right as positive:
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v_i = +20 m s⁻¹
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v_f = -12 m s⁻¹
The impulse on the ball is:
J = m(v_f - v_i)
J = 0.15 = -4.8 N s
The negative result means the impulse is directed to the left. Its magnitude is 4.8 N s.
A common error is to subtract speeds without signs and calculate 0.15(20 - 12). That ignores the reversal of direction. Rebounding generally involves a greater momentum change than merely stopping because the final momentum points in the opposite direction.
Constant force, average force, and variable force
The compact equation J = FΔt needs careful interpretation. It can be used directly when the force is constant. If force varies, F must be the average force over the stated interval.
Force situationAppropriate methodConstant forceJ = FΔtAverage force givenJ = F_avg ΔtForce-time graph givenFind the signed area between the graph and time axisForce given as a function of timeJ = ∫F dtInitial and final momentum knownJ = p_f - p_i
The integral expression is the general definition:
J = ∫ F_net dt
In graphical terms, this means that impulse is the signed area under a force-time graph. A section above the time axis contributes positive impulse, while a section below it contributes negative impulse according to the chosen axis.
This interpretation is especially useful in collisions. Contact force often rises rapidly from zero, reaches a peak, and then falls again. Multiplying the peak force by the complete contact time would usually overestimate the impulse.
Students can reinforce this distinction through the focused A.2.2 linear momentum and impulse notes and linear momentum and impulse videos.
How to find impulse from a force-time graph
The area under a force-time graph has units of force multiplied by time, so it represents impulse. For simple graph shapes, use familiar area formulas and add the signed areas.
Suppose a collision force increases linearly from zero to 600 N and returns to zero over 0.008 s. The force-time graph is triangular, so:
J = ½ × base × height
J = ½ × 0.008 × 600 = 2.4 N s
The average force is then:
F_avg = J/Δt = 2.4/0.008 = 300 N
This is half the peak value because the graph is a triangle. For a trapezium, rectangle, or graph made from several sections, calculate each area separately before combining them.
If the graph crosses the time axis, keep the signs. Adding only the magnitudes gives the total unsigned area, not necessarily the net impulse or change in momentum.
Worked impulse calculations
Finding average force during a rebound
Return to the 0.15 kg ball whose velocity changes from +20 m s⁻¹ to -12 m s⁻¹. Its impulse is -4.8 N s. If contact lasts 0.012 s:
F_avg = J/Δt
F_avg = -4.8/0.012 = -400 N
The average resultant force on the ball is therefore 400 N to the left. Notice that this is an average over the contact interval, not necessarily the maximum force.
Finding the final velocity
A 2.0 kg trolley moving at +3.0 m s⁻¹ receives an impulse of -10 N s. Begin with the full impulse-momentum equation:
J = mv_f - mv_i
-10 = 2.0v_f - 2.0(3.0)
-10 = 2.0v_f - 6.0
v_f = -2.0 m s⁻¹
The negative result shows that the trolley reverses direction. Writing the equation symbolically before substitution makes this direction change easier to interpret.
Comparing different stopping times
A passenger's momentum changes by -300 kg m s⁻¹ during a collision. If the passenger stops in 0.050 s:
F_avg = -300/0.050 = -6000 N
If a restraint system increases the stopping time to 0.150 s while producing the same momentum change:
F_avg = -300/0.150 = -2000 N
Tripling the stopping time reduces the magnitude of the average resultant force to one-third. This is the central physics behind several collision-safety applications.
Practical examples of impulse
Airbags, seat belts, and crumple zones
In a crash, a passenger must undergo a particular momentum change to come to rest. Airbags, seat belts, and controlled deformation increase the time over which that change occurs. Since F_avg = Δp/Δt, increasing stopping time reduces the average force for the same momentum change.
These devices do not remove the required impulse. They change how that impulse is delivered and may distribute forces over a larger area, reducing injury risk.
Catching a ball
A player moves their hands backward while catching a fast ball. This increases the stopping time, reducing the average force on the hands and ball. Holding the hands rigid would stop the ball more quickly and produce a larger average force.
Follow-through in sport
When striking a ball, maintaining force over a longer contact time can increase the impulse and therefore the ball's change in momentum. A follow-through does not create impulse merely because the visible motion continues after contact. Its relevance is that good technique may help sustain an effective force during the actual contact interval.
Landing and protective surfaces
Bending the knees when landing and using padded mats increase the time over which downward momentum is reduced. For a given change in momentum, a longer stopping interval reduces average force. A complete force analysis may also need to include weight, because impulse is based on the resultant force, not automatically the contact force alone.
Impulse and collisions are not the same as momentum conservation
Impulse-momentum analysis follows one object or a defined system and connects external resultant force to momentum change:
J_external = Δp_system
Momentum conservation concerns the total momentum of a system. Total momentum remains constant when the net external impulse on that system is zero or negligible during the interaction.
During a collision, two objects exert equal and opposite forces on each other for the same contact time. They therefore experience equal and opposite impulses. Momentum transferred from one object is gained by the other, while the total momentum of the two-object system remains unchanged if external impulse is negligible.
This does not mean each object's momentum remains constant. Each object can undergo a substantial momentum change even while the system's total momentum is conserved. The A.2.3 collisions and explosions notes develop that system-level analysis further.
Common IB Physics mistakes with impulse
Using force instead of resultant force
The equation connects momentum change to net impulse. If the problem includes weight, drag, thrust, normal force, or another external force, decide whether it is included, negligible, or already accounted for in the stated resultant force.
Treating velocity as an unsigned speed
Momentum and impulse are vectors. Choose a positive direction before substituting numbers, especially when an object rebounds.
Multiplying peak force by contact time
For a changing force, use the graph's area or the average force. Peak force multiplied by the entire interval is generally incorrect unless the force truly remains at that peak.
Using the wrong time unit
Milliseconds must be converted into seconds. For example, 8.0 ms = 0.0080 s, not 0.08 s.
Assuming momentum is always conserved
Momentum conservation applies to a defined system when its net external impulse is zero or negligible. It is not an unrestricted statement about every individual object.
Confusing impulse with force
Impulse is not a force. Force measures the rate of change of momentum, while impulse measures the accumulated effect of force over time.
The IB Physics forces and momentum common-mistakes guide provides further examples of these errors.
An exam method for impulse questions
Use the following sequence under timed conditions:
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Define the object or system. Decide whose momentum is changing.
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Choose a positive direction. Mark velocity and force directions clearly.
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Convert to SI units. Pay particular attention to grams and milliseconds.
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Select the appropriate form. Use force-time, graph area, or change in momentum depending on the data.
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Write the symbolic equation first. For example, F_avg Δt = m(v_f - v_i).
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Substitute signed values. Do not remove negative velocities.
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State units and direction. Interpret a negative answer using the chosen axis.
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Check plausibility. A shorter collision time should imply a larger average force for the same impulse.
Once the idea is secure, active practice matters more than rereading. RevisionDojo's A.2 Forces and Momentum Questionbank can be used for targeted calculations, while the A.2 Forces and Momentum flashcards help consolidate definitions and equations. Jojo AI can help identify whether an error came from the physics, vector signs, units, or algebra.
Conclusion
Impulse is the product of force and the time for which it acts, provided the force is constant or represented by an average value. Its deeper meaning is the change in momentum, expressed by J = Δp. For a variable force, impulse is the signed area under a force-time graph.
Successful IB answers define a direction, use the resultant force, preserve vector signs, and distinguish an individual object's momentum change from conservation of momentum for a system. RevisionDojo's A.2 notes, Questionbank, flashcards, and Jojo AI are useful next steps for turning these principles into reliable exam technique.
