Instantaneous Acceleration Examples, Definition & Formula
Instantaneous Acceleration Examples
Understanding the concept of instantaneous acceleration is important in understanding the physics of motion. Instantaneous acceleration is the rate at which an object’s velocity changes at any given moment. It’s different than average acceleration, which is the rate at which an object’s velocity changes over a given period.
Here, we’ll take a look at seven examples of instantaneous acceleration found in everyday life. Each example will help you understand the concept of instantaneous acceleration and how it applies to physics.
But before you read any further, it might be a good idea to briefly understand the concept of instantaneous acceleration. It will help you to get important insight, so you can understand the examples better. If you want to skip, you can skip by clicking on the link below.
Instantaneous acceleration Definition in brief
It is the rate of change of an object’s velocity at a specific moment in time. It describes how quickly the velocity of an object is changing at a specific instant, rather than over a longer period.
For example, when a car accelerates from 0 to 60 mph, its velocity changes rapidly from 0 to 60 mph in a short amount of time, resulting in instantaneous acceleration.
In the above example, the velocity of the object changes rapidly in a short amount of time, resulting in instantaneous acceleration.
Instantaneous acceleration Formula
The formula for instantaneous acceleration is given as:
a = (v(f) – v(i)) / t where 
To calculate instantaneous acceleration, you need to know the initial velocity, final velocity, and the time interval over which the velocity changes.
Here’s a numerical example to demonstrate how to calculate instantaneous acceleration:
Suppose a car is initially at rest and accelerates to a speed of 30 meters per second (m/s) in 5 seconds. To find the car’s instantaneous acceleration at the 2second mark, we can use the formula:
a = (v(f) – v(i)) / t
where
(initial velocity) v (i)= 0 m/s,
(final velocity) v (f) = 30 m/s,
and (time) t = 2 seconds.
After putting these values into the formula, we get:
a = (30 m/s – 0 m/s) / 2 s
a = 15 m/s^{2}
Therefore, the car’s instantaneous acceleration at the 2second mark is 15 m/s^{2}. This means that the car’s velocity is increasing by 15 m/s every second.
The instantaneous acceleration would be different at other points in time, depending on how the car’s velocity is changing over time.
7 Instantaneous Acceleration Examples in real life
I hope the explanation of instantaneous acceleration provided earlier has been clear and easy to understand. Now let us look at the examples to understand more clearly.
Examples

The car accelerates from 0 to 60 mph

A car at a traffic light suddenly accelerates when the light turns green

The ball is dropped from a height

A person jumping off a diving board

Roller coaster going down a hill

Airplane taking off

Rocket being launched
In the following paragraph, I will provide a brief explanation of each example mentioned earlier.

A car accelerating from 0 to 60 mph:
When a car accelerates from 0 to 60 mph, it experiences instantaneous acceleration because its velocity changes rapidly from 0 to 60 mph. The acceleration is not constant but increases quickly as the engine applies force to the wheels, propelling the car forward. 
A car at a traffic light that suddenly accelerates when the light turns green:
Initially, when the car is stopped at the traffic light, its velocity is zero. However, when the traffic light turns green, the driver applies force to the car’s gas pedal, which increases the car’s speed rapidly. The change in velocity from zero to some positive value over a very short period represents instantaneous acceleration. 
A ball being dropped from a height:
When a ball is dropped from a height, it initially has zero velocity. However, as it falls, its velocity rapidly increases due to the force of gravity, resulting in instantaneous acceleration. 
A person jumping off a diving board:
When a person jumps off a diving board, their velocity changes rapidly due to the force of gravity. The person initially has zero velocity while standing on the board, but once they jump, their velocity increases quickly, resulting in instantaneous acceleration. 
A roller coaster going down a hill:
As a roller coaster goes down a hill, its velocity increases rapidly due to the force of gravity, resulting in instantaneous acceleration. 
An airplane taking off:
During takeoff, an airplane initially accelerates uniformly, meaning that its velocity increases at a constant rate over time. However, the takeoff also involves instantaneous acceleration because the velocity of the airplane changes rapidly from zero to a much higher speed in a short amount of time.
Now, the last instantaneous acceleration example in our blog is a rocket being launched

A rocket being launched:
Like the airplane taking off, the rocket initially accelerates uniformly, but once it reaches a certain height and speed, the acceleration becomes instantaneous as the rocket reaches higher speeds and greater altitudes in a shorter amount of time. This results in rapid changes in velocity, which is an example of instantaneous acceleration.
For further information, you can refer to the following resources:
References
 The University of Central Florida Open Textbook –
Chapter 3.3: Average and Instantaneous Acceleration https://pressbooks.online.ucf.edu/osuniversityphysics/chapter/33averageandinstantaneousacceleration/
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