A Level Physics: Impulse — The Tiny Moment That Changes Everything
A tennis ball may be in contact with a racket for only a few thousandths of a second. Yet during that tiny interval, the ball can change direction completely and leave the racket travelling at more than 100 miles per hour.
How can such a short contact produce such a dramatic change in motion?
The answer lies in one of the most useful ideas in A Level Physics: impulse.
Impulse connects force, time and momentum. It helps us explain tennis serves, football kicks, car crashes, airbags, rocket engines, jumping, landing and even the way we package delicate objects.
It is also an excellent example of how physics can reveal what is happening during an event that takes place far too quickly for us to see clearly.
What Is Impulse?
Impulse is the product of force and the time for which that force acts.
For a constant force:
Impulse = force × time
J = FΔt
Impulse is also equal to the change in momentum of an object:
J = Δp
Therefore:
FΔt = mv − mu
where:
m = mass
u = initial velocity
v = final velocity
F = average force
Δt = time for which the force acts
This gives us the impulse–momentum relationship:
Impulse = change in momentum
The unit of impulse is the newton second:
N s
This is equivalent to:
kg m s⁻¹
That is not a coincidence. Momentum and impulse have the same units because an impulse produces a change in momentum.
Why Time Matters
Students often concentrate on the size of the force and overlook the importance of time.
However, the same change in momentum can be produced by:
• a large force acting for a short time
• a smaller force acting for a longer time
Rearranging the impulse equation gives:
Average force = change in momentum ÷ time
F = Δp ÷ Δt
This means that, for a fixed change in momentum, increasing the time reduces the average force.
This simple relationship explains a remarkable number of everyday situations.
Catching a Ball Safely
Imagine catching a fast-moving cricket ball.
If you hold your hands rigid and stop the ball almost instantly, the stopping time is very short. The force on your hands will therefore be large.
An experienced player moves their hands backwards while catching the ball. The ball still comes to rest, so the change in momentum is the same, but it is brought to rest over a longer time.
Increasing the stopping time reduces the average force.
The player is not removing the impulse. The impulse must still equal the ball’s change in momentum. They are spreading that impulse over a longer period.
The same principle explains why gymnasts bend their knees when landing and why people instinctively roll after jumping from a height.
Impulse in Tennis
Tennis provides an excellent context for studying impulse because the ball can experience a very large change in momentum during an extremely short contact time.
A tennis ball approaching a player already has momentum. When the racket strikes it, the ball may:
• slow down
• stop momentarily
• reverse direction
• leave with a much greater speed
Because momentum is a vector, direction is essential.
A ball travelling towards the player and then travelling away has undergone a much larger change in momentum than a ball that merely slows down while continuing in the same direction.
A Tennis Calculation
Suppose a tennis ball has a mass of 0.058 kg.
It approaches the racket at 20 m/s and leaves in the opposite direction at 30 m/s.
Let the direction away from the player be positive.
Initial velocity:
u = −20 m/s
Final velocity:
v = +30 m/s
The change in momentum is:
Δp = m(v − u)
Δp = 0.058 × (30 − (−20))
Δp = 0.058 × 50
Δp = 2.9 kg m s⁻¹
Therefore, the impulse delivered to the ball is:
J = 2.9 N s
If the ball is in contact with the racket for 0.005 seconds:
F = Δp ÷ Δt
F = 2.9 ÷ 0.005
F = 580 N
This is the average force. The maximum force during the collision may be considerably greater.
It is impressive to think that such a large force acts during an interval of only five milliseconds.
The Role of the Racket Strings
A modern tennis racket is not completely rigid. The strings deform when the ball strikes them, and the ball itself becomes compressed.
This deformation affects:
• the contact time
• the peak force
• the transfer of energy
• the amount of vibration
• the control the player has over the shot
Looser strings may deform more and can give a different sensation of power and control. Tighter strings usually deform less and may provide a more direct response.
However, racket performance is not determined by impulse alone. Energy transfer, string tension, racket mass, swing speed, spin and the coefficient of restitution all play a part.
Impulse tells us how much the momentum changes. It does not, by itself, tell us how efficiently energy has been transferred.
Does Following Through Increase the Impulse?
Coaches often tell players to follow through after striking the ball.
A common explanation is that following through increases the contact time and therefore increases the impulse. There is some truth in the idea that the racket must continue moving effectively through the impact, but the explanation needs care.
The ball is normally in contact with the racket for only a few milliseconds. Most of the visible follow-through happens after the ball has already left the strings.
The real value of following through is that it encourages the player to:
• maintain racket speed through the contact point
• avoid slowing the racket before impact
• produce a smoother movement
• control the direction of the shot
• reduce unnecessary strain on the arm
A good follow-through is therefore evidence of an effective stroke, rather than simply a way of keeping the ball on the racket for a visibly longer time.
Force–Time Graphs
In real collisions, the force is rarely constant.
When a tennis ball strikes a racket, the force rises rapidly, reaches a maximum and then falls as the ball leaves the strings.
Impulse is found from the area under a force–time graph.
Impulse = area under the force–time graph
This is a very important A Level Physics skill.
For a rectangular graph:
Impulse = force × time
For a triangular graph:
Impulse = ½ × base × height
For an irregular graph, the impulse may be estimated by counting squares, dividing the graph into simpler shapes or using computer data-logging software.
This is where practical physics becomes especially useful. A force sensor can record hundreds or thousands of measurements every second, revealing the shape of a collision that our eyes cannot resolve.
A Practical Investigation with a Dynamics Trolley
One useful experiment is to allow a dynamics trolley or smart cart to collide with different buffers.
Possible buffers might include:
• a rigid wooden block
• a spring
• foam
• rubber
• bubble wrap
• a magnetic bumper
A force sensor can record force against time during each collision.
Students can compare:
• maximum force
• collision time
• area under the force–time graph
• initial and final momentum
• whether momentum is conserved
• how different materials affect the peak force
A soft buffer usually increases the collision time and reduces the maximum force.
However, if the trolley undergoes the same overall change in momentum, the total impulse will be similar.
The shape of the graph changes even when the area under it remains approximately the same.
This is an important distinction:
The material can change how the force is delivered without necessarily changing the total impulse.
A Simple Ball Experiment
Impulse can also be investigated using balls dropped onto different surfaces.
A ball may be dropped onto:
• a hard floor
• carpet
• foam
• sand
• a force plate
A ball that bounces experiences a greater change in momentum than a ball that simply stops.
For example, if a ball approaches the floor with downward momentum and rebounds upwards, the direction of its momentum has reversed.
The change in momentum is therefore greater than it would be if the ball had merely come to rest.
This is why a bouncing object can produce a surprisingly large impulse on the surface.
Students can use video analysis to measure the speed immediately before and after impact. A force plate can then provide a force–time graph for comparison.
Airbags, Seat Belts and Crumple Zones
Impulse is central to vehicle safety.
In a crash, a passenger’s momentum must change. If the vehicle stops, the passenger must also be brought to rest.
The change in momentum cannot simply be avoided.
Safety systems work by increasing the time over which that change occurs.
Seat belts stretch slightly. Airbags compress. Crumple zones deform.
All these features increase the stopping time and reduce the average force acting on the occupants.
F = Δp ÷ Δt
Doubling the stopping time approximately halves the average force, provided the change in momentum remains the same.
Crumple zones also absorb energy through controlled deformation. This reminds us that both momentum and energy ideas are needed for a full explanation of a collision.
Protective Equipment in Sport
The same principle is used in:
• cycling helmets
• climbing mats
• boxing gloves
• shin pads
• cricket pads
• horse-riding body protectors
• padded goalposts
• running shoes
Padding compresses and increases the stopping time. This reduces the peak force on the body.
A helmet does not prevent the head’s momentum from changing. Instead, it aims to make that change happen over a slightly longer time while distributing the force over a wider area.
Even a few additional milliseconds can make an important difference.
Using Impulse to Produce Motion
Impulse is not only about stopping objects. It is equally important when setting objects in motion.
A sprinter pushes backwards and downwards on the starting blocks. The blocks exert an equal and opposite force on the athlete.
The longer and more strongly the athlete pushes, the greater the impulse and the greater the change in forward momentum.
The same idea applies when:
• a swimmer pushes away from the wall
• a rower drives the blade through the water
• a footballer kicks a ball
• a golfer strikes a golf ball
• a high jumper pushes against the ground
• a rocket engine produces thrust
• a propeller accelerates water backwards
To change an object’s momentum, a resultant force must act for a period of time.
Impulse in Rowing and Sailing
Impulse also has applications on the water.
A rower applies force to the water through the blade. The water is pushed backwards, and the boat gains forward momentum.
A short, violent stroke may produce a large peak force but may not always give the most controlled or effective motion. A well-timed stroke delivers force through an appropriate part of the movement.
In sailing, changes in momentum occur when:
• a boat accelerates after a tack
• a gust increases the force on the sail
• a boat collides with a wave
• a crew member moves suddenly
• a boat is brought alongside a pontoon
• a safety boat takes up the tension in a tow line
A tow line should not become tight with a sudden jerk. A sharp change in momentum over a very short time creates a large force that may damage fittings or destabilise the boats.
Allowing the force to build more gradually increases the time and reduces the peak load.
Impulse and Rockets
A rocket engine produces thrust by ejecting gas backwards at high speed.
The exhaust gases gain backward momentum. The rocket gains an equal amount of forward momentum.
Even a relatively small force can create a large change in momentum if it acts for long enough.
This is particularly important in space, where engines or thrusters may operate for extended periods. Small thrusters can gradually alter a spacecraft’s velocity, orientation or orbit.
Impulse is often used when describing rocket engines. The total impulse of an engine is the thrust multiplied by the time for which it operates.
Specific impulse is another quantity used in rocket science, although it has a specialised definition related to how effectively the engine uses propellant.
Does Impulse Improve Efficiency?
Impulse can help us analyse how effectively a force changes motion, but impulse is not the same as energy efficiency.
A system can produce the required impulse while wasting considerable energy as:
• heat
• sound
• vibration
• unwanted deformation
• turbulence
• movement in the wrong direction
For example, a tennis player may produce a large impulse, but an inefficient technique may also create unnecessary body movement, vibration and strain.
Similarly, a propeller may create thrust, but some energy may be lost in turbulence.
Efficiency is normally calculated using:
Efficiency = useful energy output ÷ total energy input
or:
Efficiency = useful power output ÷ total power input
Impulse answers the question:
“How much did the momentum change?”
Efficiency answers the question:
“How much of the input energy produced the useful result?”
The two ideas are related in practical situations, but they should not be confused.
Improving the Application of Force
In sport and engineering, we often want force to be applied:
• in the correct direction
• at the correct time
• for an appropriate duration
• without excessive peak forces
• with minimal unwanted motion
• with as little wasted energy as possible
A rower who applies force at the wrong point in the stroke may waste energy.
A tennis player who strikes the ball away from the racket’s effective hitting region may produce more vibration and less useful ball speed.
A runner whose foot lands too far ahead of their body may experience a braking impulse before producing a forward-driving impulse.
Impulse analysis can therefore help coaches and engineers understand not only whether motion changed, but how that change was produced.
My Experience of Teaching Impulse
Impulse is one of those topics that can appear rather dry when it is introduced only as:
J = FΔt
Students may learn the equation, substitute a few numbers and assume that the topic is finished.
The understanding changes when they see a real force–time graph.
A collision that looks instantaneous suddenly has a structure. The force rises, reaches a peak and falls again. Changing the bumper changes the graph. A bouncing object produces a different momentum change from one that simply stops.
Tennis is particularly useful because students already understand that the racket changes the motion of the ball. Physics gives them the language to describe exactly what has happened.
The most important step is often getting students to include direction.
A ball that reverses direction does not merely change its speed. Its velocity and momentum have changed sign. Missing that point can completely change the answer to a calculation.
Impulse also brings several parts of the A Level course together:
• Newton’s laws
• momentum
• vectors
• graphs
• collisions
• materials
• energy
• experimental data
That makes it far more than a single equation to memorise.
Common Mistakes to Avoid
Students commonly lose marks by:
• ignoring the direction of velocity
• using speed instead of velocity
• forgetting that momentum is a vector
• calculating mv − mu incorrectly when u is negative
• using the maximum force instead of the average force
• treating every force–time graph as a rectangle
• confusing impulse with energy
• assuming a longer stopping time reduces the total impulse
• forgetting that a rebound creates a larger momentum change
A reliable method is:
Choose a positive direction.
Write each velocity with its correct sign.
Calculate the initial momentum.
Calculate the final momentum.
Find final momentum minus initial momentum.
Use impulse = change in momentum.
Use the contact time to calculate average force if required.
Conclusion: A Small Time with a Large Effect
Impulse allows us to understand events that happen in fractions of a second.
It explains why a tennis ball can reverse direction almost instantly, why a player moves their hands backwards when catching, why airbags save lives and why padding reduces injuries.
It also helps us investigate how forces create motion in running, rowing, swimming, vehicles and spacecraft.
The central idea is simple:
Impulse = change in momentum
Yet behind that simple equation lies a powerful way of thinking.
We cannot always avoid a change in momentum. A ball must be stopped, a passenger must be restrained and an athlete must push against the ground.
What we can control is how the force is applied, how long it acts and in which direction it acts.
That is where impulse becomes more than an examination equation. It becomes a practical tool for understanding sport, safety, motion and engineering.



