Acceleration
5. Acceleration in the Real World
Learning outcomes
- I can identify examples of acceleration in transportation, sports, and nature.
- I can explain the role of acceleration in vehicle performance.
- I can analyze acceleration data from real-world situations.
- I can relate acceleration to safety features such as seat belts and airbags.
- I can apply acceleration concepts to practical problem-solving situations including free fall and terminal velocity.
Acceleration in the Real World
Acceleration is not just something we calculate in physics problems. It occurs whenever an object's velocity changes, making it important in transportation, sports, engineering, nature, and safety.
Remember:
Acceleration is the rate of change of velocity.
An object accelerates whenever it:
- speeds up
- slows down
- changes direction
- changes both speed and direction
This means acceleration occurs in far more situations than simply a car pressing its accelerator.
Acceleration in Transportation
Vehicles constantly experience acceleration.
Consider a car travelling through a city.
The car may:
Start from rest → Speed up → Travel at constant velocity → Brake → Turn → Stop
Acceleration occurs during every stage except when the car travels at a constant velocity in a straight line.
Examples include:
- cars leaving traffic lights
- buses braking at stops
- aircraft taking off
- trains leaving stations
- bicycles turning corners
- roller coasters changing speed and direction
Vehicle Performance
Acceleration is an important measure of vehicle performance.
A car that changes velocity from: 0 m/s to 25 m/s in 5 seconds has an average acceleration of:
\( a = \frac{ \Delta v }{ \Delta t } = \frac{\ 25 - 0}{5} = 5m/s^2 \)
This means the car's velocity increases by an average of 5 m/s every second.
Comparing Vehicle Acceleration
Suppose two cars accelerate from rest.
Car A
Reaches 20 m/s in 4 seconds.
\( a = \frac{20}{4} = 5m/s^2 \)
Car B
Reaches 20 m/s in 8 seconds.
\( a = \frac{20}{8} = 2.55m/s^2 \)
Car A has the greater average acceleration.
It changes its velocity more rapidly.
This is why acceleration times such as 0–100 km/h are often used when comparing vehicle performance.
Acceleration and Braking
Braking also involves acceleration.
Suppose a car is travelling at: 24 m/s and stops in 6 s.
Its acceleration is:
\( a = \frac{0 - 24}{6} = -4m/s^2 \)
The negative sign indicates that the acceleration acts opposite to the chosen positive direction of motion.
Because the car's speed is decreasing, we can also describe this as deceleration.
Acceleration While Turning
A vehicle can accelerate even when its speed remains constant.
Imagine a car travelling around a roundabout at a constant: 10m/s
Its speed remains the same, but its direction continuously changes.
Since velocity includes direction:
Changing direction → changing velocity
Therefore: The car is accelerating
This inward acceleration during circular motion is called centripetal acceleration.
Acceleration in Sports
Sports provide many excellent examples of acceleration.
An athlete accelerates whenever they change their speed or direction.
Examples include:
- a sprinter leaving the starting blocks
- a football player changing direction
- a cyclist accelerating out of a corner
- a tennis ball changing velocity after being struck
- a basketball falling toward the floor
- a diver accelerating toward the water
- a skier travelling around a turn
A Sprinter
A sprinter starts from rest and reaches: 10 m/s after 2.5 s
Average acceleration:
\( a = \frac{10 - 0}{2.5} = 4m/s^2 \)
The sprinter's velocity increases rapidly during the beginning of the race.
Later, the runner may reach approximately constant speed.
At that stage: a ≈ 0
provided the runner is moving in a straight line at approximately constant speed.
Changing Direction in Sports
Imagine a football player running east at: 6 m/s
The player suddenly turns and begins running north at the same speed.
Has the player accelerated?
Yes.
The speed is still: 6 m/s
but the direction has changed.
Therefore the velocity changed.
This demonstrates again that:
Acceleration does not require a change in speed.
Acceleration Data
Real motion can be analysed using data collected from:
- speed sensors
- GPS devices
- motion detectors
- accelerometers
- smartphones
- vehicle computers
Consider the following measurements from a cyclist:
| Time (s) | Velocity (m/s) |
|---|---|
| 0 | 2 |
| 2 | 6 |
| 4 | 10 |
| 6 | 10 |
| 8 | 6 |
| 10 | 2 |
We can use the data to analyse the cyclist's motion.
Analysing the Cyclist's Data
0–4 seconds
Velocity increases: 2 → 10 m/s
Average acceleration:
\( a = \frac{10 - 2}{4} = 2m/s^2 \)
The cyclist is speeding up.
4–6 seconds
Velocity remains: 10 m/s
Therefore: a = 0
The cyclist moves at constant velocity.
6–10 seconds
Velocity changes: 10 → 2 m/s
\( a = \frac{2 - 10}{4} = -2m/s^2 \)
The cyclist is slowing down.
Acceleration and Vehicle Safety
Acceleration is extremely important when considering vehicle collisions.
During a collision, a vehicle may change from a large velocity to zero in a very short time.
For example, suppose a vehicle travelling at: 20 m/s stops in 0.10s
Average acceleration:
\( a = \frac{0 - 20}{0.10} = -200m/s^2 \)
This is an extremely large acceleration magnitude.
Large accelerations during collisions can produce large forces on passengers.
Why Increasing Stopping Time Helps
From:
\( a = \frac{ \Delta v }{ \Delta t } \)
we can see that for the same change in velocity:
Larger stopping time → Smaller acceleration magnitude
For example, consider the same velocity change:
20 m/s → 0
Stopping in 0.10 s
a = -200 m/s2
Stopping in 0.50 s
a = -40 m/s2
Increasing the stopping time dramatically reduces the magnitude of the acceleration.
This principle is central to many vehicle safety systems.
Seat Belts
When a vehicle suddenly stops, passengers tend to continue moving because of their inertia.
A seat belt restrains the passenger and helps bring the passenger to rest with the vehicle.
Modern seat belts can also work with other safety systems to manage the forces acting on the body during a collision.
Without a seat belt, the passenger may continue moving until striking the:
- dashboard
- steering wheel
- windscreen
- seat in front
The seat belt helps control this rapid change in velocity.
Airbags
Airbags provide another way of reducing injury during a collision.
The airbag inflates rapidly and provides a surface that helps bring the passenger to rest over a greater time and distance than a hard dashboard or steering wheel would.
For the same change in velocity:
Longer stopping time → Smaller acceleration magnitude
This can reduce the force acting on the passenger.
Airbags are designed to work with seat belts, not replace them.
Crumple Zones
Cars also contain crumple zones.
These parts of the vehicle are designed to deform during a collision.
The deformation:
- absorbs and redirects some energy
- increases the time over which the vehicle changes velocity
- reduces the magnitude of the acceleration experienced by the passenger compartment compared with a more abrupt stop
This demonstrates how understanding acceleration can directly influence engineering and safety design.
Acceleration in Nature
Acceleration also occurs throughout nature.
Examples include:
- falling objects
- rain falling toward Earth
- rocks rolling down hills
- animals running and turning
- ocean waves moving objects
- planets orbiting stars
- moons orbiting planets
- meteors falling through atmospheres
One of the most important natural examples is free fall.
Free Fall
An object is in free fall when gravity is the only significant force acting on it.
Near Earth's surface, the acceleration due to gravity is approximately:
g = 9.8 m/s2
directed downward.
In introductory calculations, this is sometimes rounded to:
g ≈ 10 m/s2
This means a freely falling object's downward velocity changes by approximately 9.8 m/s every second.
h(t) = ho + vot − ½gt2
Falling from Rest
Suppose a ball is dropped from rest and we ignore air resistance.
Its approximate downward velocities would be:
| Time | Downward Velocity |
|---|---|
| 0 s | 0 m/s |
| 1 s | 9.8 m/s |
| 2 s | 19.6 m/s |
| 3 s | 29.4 m/s |
| 4 s | 39.2 m/s |
The velocity increases by 9.8 m/s each second.
Therefore, its acceleration is 9.8 m/s2 downward
Does a Falling Object Keep Accelerating Forever?
The simple free-fall model assumes there is no air resistance.
Real objects falling through Earth's atmosphere experience another force:
drag, or air resistance.
Drag acts opposite to the direction of motion.
As a falling object becomes faster, air resistance generally becomes larger.
Terminal Velocity
Consider a skydiver falling through the atmosphere.
Initially:
Weight > Air resistance
There is a downward net force.
Therefore the skydiver accelerates downward.
As speed increases:
Air resistance increases
Eventually: Air resistance = Weight
The forces are balanced.
Therefore: Fnet = 0 and: a = 0
The skydiver continues falling at a constant velocity called terminal velocity.
Terminal Velocity Does Not Mean Stopping
This is an important distinction.
At terminal velocity: a = 0 but v ≠ 0
The object is still moving.
Its velocity simply stops changing.
Therefore: Zero acceleration does not mean zero velocity.
Opening a Parachute
When a skydiver opens a parachute, the surface area exposed to the air increases dramatically.
This produces much greater drag.
Immediately after the parachute opens: Drag > Weight
The net force acts upward while the skydiver is still moving downward.
Therefore, the skydiver's downward speed decreases.
Eventually, the forces balance again: Drag = Weight
The skydiver reaches a new, much lower terminal velocity.
A Terminal-Velocity Journey
A skydiver's motion can be divided into several stages.
Stage 1 – Jump
Velocity is initially small.
Gravity produces a downward acceleration.
Stage 2 – Speed Increases
The skydiver becomes faster.
Air resistance increases.
Stage 3 – First Terminal Velocity
Drag equals weight. a = 0
Velocity becomes approximately constant.
Stage 4 – Parachute Opens
Drag suddenly becomes much larger.
The skydiver slows rapidly.
Stage 5 – New Terminal Velocity
Drag and weight become balanced again.
The skydiver continues downward at a much slower constant velocity.
Solving Practical Acceleration Problems
Consider a motorcycle that increases its velocity from: 8 m/s to 26 m/s in 6 s
Step 1 – Find the velocity change
Δv = 26 - 8 = 18 m/s
Step 2 – Divide by time
\( a = \frac{18}{6} = 3 m/s^2 \)
Interpretation:
The motorcycle's velocity increases by an average of 3 m/s each second.
Practical Problem: Braking
A cyclist travelling at 12 m/s brakes and stops in 3s.
Calculate the acceleration.
\( a = \frac{0 - 12}{3} = -4m/s^2 \)
The negative acceleration shows that the velocity is decreasing in the chosen positive direction.
Practical Problem: Free Fall
A stone is dropped from rest.
Ignoring air resistance, estimate its velocity after 3 s.
Using:
vf = vi + at
we have:
vi = 0
a = 9.8 m/s2 downward
Therefore:
vf = (0) + (9.8)(3) = 29.4 m/s downward
Using Acceleration Data to Make Decisions
Acceleration data can help answer practical questions.
For example:
Which car accelerates faster?
Compare changes in velocity over equal times.
Which cyclist brakes more sharply?
Compare the magnitudes of their negative accelerations.
When has a falling object reached terminal velocity?
Look for the point when velocity becomes constant and acceleration becomes zero.
Why can airbags reduce injuries?
They help increase the stopping time and distance, reducing the magnitude of acceleration and the force experienced.
This shows how mathematical calculations can help us interpret real physical situations.
Reading Acceleration from a Velocity-Time Graph
Acceleration can also be determined graphically.
On a velocity-time graph: slope = acceleration
A steep upward slope indicates a large positive acceleration.
A horizontal line indicates: a = 0
A downward slope indicates negative acceleration.
This makes velocity-time graphs particularly useful when analysing experimental or real-world motion data.
Acceleration and Forces
Acceleration is produced when there is a net force acting on an object.
Newton's Second Law describes this relationship:
Fnet = ma
Therefore, for a particular mass:
Larger net force → Larger acceleration
This connects acceleration to:
- vehicle engines
- braking
- collisions
- falling objects
- sports
- rockets
- turning vehicles
Common Misconceptions
Acceleration does not only mean speeding up.
Slowing down and changing direction are also forms of acceleration.
Negative acceleration does not automatically mean moving backward.
It describes the direction of acceleration relative to the chosen coordinate system.
A falling object does not necessarily accelerate forever.
Air resistance can eventually produce terminal velocity.
Terminal velocity is not zero velocity.
At terminal velocity: v = constant
and: a = 0
Seat belts and airbags do not prevent the passenger's velocity from changing.
Instead, they help manage how the passenger comes to rest and reduce the severity of the forces involved.
Did You Know?
Accelerometers are built into many smartphones.
They can detect changes in motion and orientation and contribute to features such as:
- screen rotation
- motion tracking
- fitness measurements
- gaming controls
- vehicle-motion detection
The same fundamental quantity studied in classroom physics—acceleration—is being measured continuously by devices people carry every day.
Key Terms
Acceleration – Rate of change of velocity.
Deceleration – A decrease in speed.
Free fall – Motion in which gravity is the only significant force acting on an object.
Gravity – The attractive force between masses.
Acceleration due to gravity (g) – Approximately 9.8 m/s2 downward near Earth's surface.
Air resistance – A drag force that opposes motion through air.
Terminal velocity – Constant falling velocity reached when drag balances weight.
Net force – The overall force resulting from all forces acting on an object.
Crumple zone – A vehicle structure designed to deform during a collision and help increase stopping time while managing energy.
Accelerometer – A sensor used to measure acceleration.
Key Takeaways
- Acceleration occurs whenever velocity changes.
- Real-world acceleration occurs in transportation, sports, nature, and technology.
- Vehicles accelerate when they speed up, slow down, or turn.
- Acceleration data can be calculated using: \( a = \frac{ \Delta v }{ \Delta t } \)
- Vehicle performance can be compared using acceleration measurements.
- Large changes in velocity over very short times can produce large acceleration magnitudes.
- Seat belts, airbags, and crumple zones help manage rapid changes in velocity during collisions.
- Increasing stopping time can reduce the magnitude of acceleration and therefore help reduce forces on passengers.
- Athletes accelerate when they change speed or direction.
- Objects in free fall near Earth's surface accelerate at approximately: 9.8 m/s2 downward when air resistance is neglected.
- Real falling objects experience air resistance.
- Terminal velocity occurs when drag balances weight.
- At terminal velocity, acceleration is zero, but the object is still moving.
- Opening a parachute increases drag and produces a much lower terminal velocity.
- Acceleration can be analysed using calculations, data tables, and velocity-time graphs.
- Understanding acceleration helps us solve practical problems involving vehicles, collisions, sports, free fall, and falling objects.