Uniform Acceleration

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Introduction

To identify the laws that govern the various changes that take place in bodies with respect to time, we must be able to describe the changes and have some way to record them for the future references. The simplest way to observe a body is the apparent changes in its position with respect to time, which is known as the motion of that object under observation. The rate of change of displacement of the object is known as the velocity of the object. 

The next step in developing the equations of motion is to introduce another important concept that goes beyond the concept of velocity to that of change of velocity. The rate of change of velocity is known as the Acceleration of the particle. In this article, we will learn about what is uniformly accelerated motion in detail.


What is Uniform Acceleration

We know that acceleration is the rate of change of velocity with respect to time. Acceleration is a vector quantity and the direction of acceleration will be the same as the direction of the rate of change of velocity. The SI unit of acceleration is m/s2 and the dimensions of acceleration are  [ M0 L1T -2 ].

We are familiar with the concept of uniform motion, if an object covers equal displacement in an equal interval of time it is said to be undergoing uniform motion. Now the question is what is meant by uniform acceleration? 


Define Uniform Acceleration

To answer define uniformly accelerated motion, let us first understand what is a uniformly accelerated motion in detail. As the name itself suggests uniformly accelerated motion means the object or a body is possessing a constant acceleration. Constant acceleration doesn’t mean zero velocity.  So the definition of uniform acceleration or uniform acceleration definition states that- if a body is under motion such that the amount of change in its velocity in equal intervals of time will be constant. 

In other words, the uniform acceleration motion definition is when an object is moving in a straight line and its change in velocity over a period of time or interval remains constant. From the uniformly accelerated motion definition, we understand that the uniform acceleration can be witnessed in a straight line motion.

For acceleration is a uniform example, the motion of the freely falling body, the acceleration of the body will be the only acceleration due to gravity. If we plot a graph of velocity versus the time we get a straight line the whole slope will give the required acceleration.


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Now, a few more example of uniform acceleration are as listed below:

  1. A ball rolling down the slope.

  2. When a bicycle rider is riding the bicycle on the slope where both the pedals are engaged.

  3. A kid sliding down from the slider, etc...

Equations of Motion:

The equation of motion for uniform acceleration are as follows:

1. The distance formula:

⇒ S = ut + ½ at2

Where,

u - The initial velocity of the body

a - Acceleration of the body

t - The time interval

2. The equation of velocity:

⇒ v = u + at

Where,

v - The final velocity of the body

u - The initial velocity of the body

a - Acceleration of the body

t - The time interval

And, we also have another equation for velocity in terms of displacement:

⇒ v2 = u2 + 2as

Where,

v - The final velocity of the body

u - The initial velocity of the body

a - Acceleration of the body

s - The distance covered

Characteristics of Uniformly Accelerated Motion:

  • If the direction of both acceleration and the change in velocity is the same then it will result in positive acceleration. 

  • At the same time if the direction of acceleration and the change in velocity is different or in the opposite direction then it will result in negative acceleration known as retardation or deceleration. 

  • With positive acceleration, the speed of the object will either increase or decrease and with the negative acceleration, speed of the object will be slowed down, hence it is known as retardation.

Note:

Now, the question that must be answered to understand uniform acceleration in detail is Is uniformly accelerated motion uniform motion? Are uniform acceleration and uniform motion the same?

The answer to this question is uniform motion and uniform acceleration are completely different from each other.  We know that when an object covers equal displacement in an equal interval of time it is said to be undergoing uniform motion, whereas the uniform acceleration is when an object is moving in a straight line and its change in velocity over a period of time will not change or remain constant. 

Therefore we should always keep in mind that uniform acceleration is not the same as uniform motion.


Non-Uniform Acceleration

The non-uniform acceleration refers to the opposite of uniform acceleration. We know that uniform acceleration means that acceleration remains constant, its change in velocity will be constant over a period of time. Whereas in the nonuniform acceleration the change in velocity will not be the same. The direction of velocity and the magnitude of the acceleration will be changing with time.

For example, in our everyday life we see that while driving a car or bike in a curved path or in heavy traffic, the velocity of the vehicle will change continuously. If we plot a graph of velocity versus the time we get a non-uniform curve.


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Examples:

1. A Man Starting At Rest Travels 30m With a Constant Acceleration of 10 m/s2 How Long Does it Take?

Sol: A man is starting his journey from the rest, then the initial velocity of the man will be zero. It is given that man travels a distance of 30m with a constant acceleration of 10 m/s2

Now, we are asked to calculate the time taken to cover this distance.

We know that from the equation of motion,

⇒ S = ut + ½ at2

Where,

u - The initial velocity of the body

a - Acceleration of the body

t - The time interval

Substituting the given values in the above equation we get,

⇒ 30 = 0 + ½ (10)t2

⇒ 5t2 = 30 

⇒ t2 = 6 

⇒ t = 2.45s

Therefore, it takes 2.45s to cover this distance.

2. A Car Starting From the Rest Accelerated at 9 m/s2 For 9 Seconds. 

  1. What Will Be the Position of the Car at the End of 9 Seconds? 

  2. What Will Be the Velocity of the Car at the End of 9 Seconds?

Sol: Given that a car is accelerating at a constant acceleration of 9 m/s2 for 9 seconds.

  1. We are asked to calculate the position of the car at the end of 9 seconds.

The initial velocity of the car is zero, as it is given that it’s starting from the rest. Let us assume that its initial position is zero. 

Let X be the position of the car at the end of 9 seconds.

From the equation of motion we have,

⇒ S = ut + ½ at2 ….(1)

Where,

u - The initial velocity of the body

a - Acceleration of the body

t - The time interval

Substituting the given data in the equation (1) we get,

⇒ X = 0 + ½ (9)(9)2

⇒ X = 364.5m

Therefore, the position of the car at the end of 9seconds is 364.5m away from the initial position.

  1. The second part of the question requires the velocity of the car at the end of the 9 seconds. It is given that, The initial velocity of the car is zero, as it is given that it’s starting from the rest. Let us assume that its initial position is zero. 

Now, from the equation of motion we have:

⇒ v = u + at ….(1)

Where,

v - The final velocity of the body

u - The initial velocity of the body

a - Acceleration of the body

t - The time interval

Substituting given values in the equation (1) we get,

⇒ v = 0 + (9)(9) = 81 m/s

Therefore, the velocity of the car at the end of 9 seconds is 81 m/s.

FAQ (Frequently Asked Questions)

1. If an Object Has Zero Acceleration it Means that the Object is Not Under Motion?

Ans: No. Zero acceleration refers to the uniform velocity. An object can have zero acceleration and still be under motion.

2. Give an Example of Uniform Acceleration.

Ans: A free-falling body is an example of uniform acceleration, a ball rolling down the slide.