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Uniform Acceleration

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Uniformly Accelerated Motion or Uniform Acceleration in Physics is a motion in which the object is accelerated at constant acceleration. We have to keep in mind that uniform accelerated motion does not mean uniform velocity i.e. in uniform accelerated the velocity of the object increases linearly with time. An object drop from the top of the roof, a ball rolling downhill, a man jumping from an airplane, etc. are all instances of uniformly accelerated motion. It is crucial to note that due to the interference of gravity or friction, many instances of uniform application do not maintain absolute uniformity of acceleration.

In this article, we will learn about, uniform acceleration, uniform accelerated motion, uniform accelerated motion equations, and others in detail.

What is Uniform Acceleration?

If the rate of change of velocity remains constant then the object is said to be in state of Uniform Acceleration. 

As we know acceleration is a vector quantity thus, the direction of motion remains the same in the case of constant acceleration.

Uniform Acceleration Examples

Some Examples of Uniformly accelerated motion are mentioned below:

  • Free-falling object under the force of gravity.
  • A ball rolling down a frictionless slope.
  • A bicycle rolling downhill when the brakes are applied.

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Uniform Accelerated Motion Formula

There are three formula that are explained by uniform accelerated motion. These formulas are used to explain the motion of an object. The three uniform accelerated motion formula are,

  • v = u + at
  • s = ut + 1/2at2
  • v2 = u2 + 2as

Uniform Acceleration Graphs

The uniform acceleration graphs is a straight line graphs. The uniform acceleration graphs is added below,

Uniform-acceleration-graph

Non-Uniform Acceleration Graphs

The non-uniform acceleration graph is the graph added below,

Non-uniform-acceleration-graphs

Kinematic Equations for Uniformly Accelerated Motion

Kinematic Equations for Uniformly Accelerated Motion provide a relation between initial velocity, acceleration, final velocity, distance covered, and time taken by the object. Let’s take the initial velocity of an object as “u”, the constant acceleration applied to the object is “a”, and the final velocity achieved by the object under this acceleration is “v” velocity the time taken is “t” and the distance covered is “s”.

First Equation of Motion (Velocity Equation)

First Equation of Motion or Velocity Equation provides the relation between final and initial velocities, acceleration, and time, it is given by,

v = u + at

where,

  • v is the final velocity
  • u is the initial velocity
  • a is the acceleration
  • t is the time taken by object

Second Equation of Motion (Distance Equation)

Second Equation of Motion or Distance Equation provides the relation between initial velocities, distance, acceleration, and time, it is given by,

s = ut + 1/2 at2

where,

  • s is the distance
  • u is the initial velocity
  • a is the acceleration
  • t is the time taken by the object

Third Equation of Motion

Third Equation of Motion provides the relation between final and initial velocities, distance, and acceleration, it is given by,

v2 = u2 + 2as

where,

  • s is the distance
  • v is the final velocity
  • u is the initial velocity
  • a is the acceleration

While using these equations sign convention must be followed. If one direction is taken to be positive then the other is taken as negative. A body in free fall can be considered to be in Uniform Accelerated Motion the body in free fall experiences the uniform acceleration of earth’s gravity. Generally, the upward motion of the object is considered to be positive whereas, the downward motion is considered to be negative.

Learn more about, Equation of Motion

Uniformly Accelerated Motion In A Plane

Projectile motion is an example of Uniformly Accelerated Motion in a Plane. Projectile motion accelerates uniformly under the force of gravitation. As we know that gravity works only in a vertical direction i.e. in the y-direction the motion in the x-direction is of constant velocity. Thus, we see that projectile motion can be broken into two different motions, and the equation of motion is calculated separately in these two motions.

Uniformly Accelerated Motion is the motion of an object when the acceleration of the object remains constant. It can be in one dimension, two dimensions, or three dimensions.

V-T Graph for Uniform Accelerated Motion

In uniform accelerated motion the velocity of the object changes at constant speed. The graph for the same is added below,

V-T-Graph-for-Uniform-Accelerated-Motion

Also, Read

Examples on Uniform Accelerated Motion

Example 1: If a body is moving at an acceleration of 2 m/s2. If the initial speed was 15m/s, what will be the speed in 5 seconds? 

Solution: 

Given,

  • u = 15m/s
  • a = 2 m/s2
  • t = 5 

For finding out the value of “v”, first equation of motion can be used. 

v = u + at 

Plugging the values in this equation, 

v = u + at 
   = 15 + (2)(5) 
   = 15 + 10 
   = 25 m/s

Example 2: If a body is moving at an acceleration of -5 m/s2. If the initial speed was 30m/s, what will be the distance co in 5 seconds? 

Solution: 

Given,

  • u = 40m/s
  • a = -5 m/s2
  • t = 5 

For finding out the value of “v”, the first equation of motion can be used. 

v = u + at 

Plugging the values in this equation, 

v = u + at 
   = 30 – (5)(5) 
   = 30 – 25 
   = 5 m/s 

Example 3: If a body is moving at an acceleration of -5 m/s2. If the initial speed was 40m/s, what will be the speed in 5 seconds? 

Solution: 

Given,

  • u = 40m/s
  • a = -5 m/s2
  • t = 5 

For finding out the value of “s”, the first equation of motion can be used. 

s = ut + 1/2a(t)2

Plugging the values in this equation,

s = ut + 1/2a(t)2

s = (40)(5) + 1/2(-5)(5)2

s = 200 + (-125/2)

s = 200 – 125/2

s = (400 – 125)/2 = 275/2

Example 4: If a body is moving at an acceleration of 10 m/s2. If the initial speed was 20m/s, what will be the speed in 2 seconds? 

Solution: 

Given,

  • u = 20 m/s
  • a = 10 m/s2
  • t = 2 

For finding out the value of “s”, the first equation of motion can be used. 

s = ut + 1/2a(t)2

Plugging the values in this equation,

s = ut + 1/2a(t)2

s = (20)(2) + 1/2(10)(2)2

s = 40 + 20 = 60 m

Example 5: A racing car catches a speed of 20m/s in 2 seconds. Find the distance covered by the car in the process. 

Solution:  

Given,

  • u = 0 m/s
  • v = 20 m/s
  • t = 2

For finding out the value of “a”, the first equation of motion can be used. 

v = u + at 

Plugging the values in this equation, 

v = u + at 

20 = 0 + (a)(2) 

20 = 2a 

a = 10 m/s2

For finding out the distance, a third equation of motion will be used

v2 = u2 + 2as

202 = 0 + 2(10)s

400 = 20s 

s = 20 m

Practice Questions on Uniform Acceleration

Q1: If the velocity of a car changes from 60 m/s to 70 m/s in 30 min and 70 m/s to 80 m/s in next 30 min. Verify if the car is in the Uniform Acceleration.

Q2: If a body starts moving at 10 m/s and its uniformly accelerates at 2m/s2. Find the distance covered by the body in 30 minutes

Q3: If the initial velocity of a bike is 45 m/s and its final velocity is 80 m/s accelerating uniformly for 10 minutes. Find the acceleration.

FAQs on Uniformly Accelerated Motion

1. Define Uniform Acceleration?

Uniform acceleration is the acceleration that does not vary with time. In such cases, the rate of change of velocity remains constant. 

2. What is Non-Uniform Motion?

An object moving with variable velocity is said to be non-uniform motion. In non uniform motion an object covers unequal distance in unequal time.

3. What is Uniformly Accelerated Motion?

Uniformly accelerated motion is defined by a motion in a straight line with a constant acceleration and zero difference.

4. What are Examples of Uniformly Accelerated Motion?

A ball rolling down a slope, a skydiver jumping out of a plane, a ball dropped from the top of a ladder, and a bicycle with its brakes engaged are all instances of uniformly accelerated motion.

5. Is Uniformly Accelerated Motion Uniform Motion?

No, uniform accelerated motion is not considered to uniform motion as in uniform motion velocity is constant whereas in uniform accelerated motion velocity is not constant.

6. What is Uniform Motion?

The motion of an object in which the object travels equal distance in equal interval of time is called the uniform motion. In uniform motion the velocity of object remains the constant.

7. When will you say a body is in Uniform Acceleration?

A body is said to be in uniform acceleration if its velocity changes at constant rate.



Last Updated : 17 Oct, 2023
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