## Motion in One Dimension-

Before you go through this article, make sure that you have gone through the previous article on Motion in One Dimension.

We have discussed-

• In one-dimensional motion, particle moves along a straight line.
• It is also known as rectilinear motion.

Various parameters related to motion are- ## Accelerated Motion-

• The motion of a particle is said to be accelerated if its velocity changes with time.
• Example- A vehicle moving on a crowded road.
• It is a kind of non-uniform motion.

## Acceleration-

 Rate of change of velocity of a particle is called as its acceleration.

Mathematically, ### Characteristics-

The characteristics of acceleration are-

• It is a vector quantity.
• Acceleration can be positive, negative or zero.
• Acceleration is zero for a moving particle if it moves with constant velocity.
• The SI unit of acceleration is meter per second2 (m/s2).
• The dimensional formula of acceleration is [M0L1T-2].

## Types of Acceleration-

There are mainly following four types of acceleration- 1. Uniform Acceleration
2. Variable Acceleration
3. Average Acceleration
4. Instantaneous Acceleration

### 1. Uniform Acceleration-

 A particle is said to be moving with uniform acceleration if equal change in velocity takes place in equal intervals of time. OR A particle is said to be moving with uniform acceleration if its velocity changes with a uniform rate.

### 2. Variable Acceleration-

 A particle is said to be moving with variable acceleration if its velocity changes equally in unequal intervals of time or unequally in equal intervals of time.

### 3. Average Acceleration-

 The average acceleration of a particle is that constant acceleration with which the particle undergoes same change in velocity in a given time as it undergoes while moving with variable acceleration during the given time.

Mathematically,

It is the ratio of total change in velocity of the particle to the total time interval in which this change in velocity takes place. Consider-

• At any time t1, the velocity of the particle is v1.
• At time t2, the velocity becomes v2.

Then for this interval, average acceleration is given by- ### 4. Instantaneous Acceleration-

 Instantaneous acceleration is the acceleration of particle at a particular instant of time.

Mathematically,

Instantaneous acceleration is the limiting value of average acceleration as the time interval becomes infinitesimally small.

If  Δv is the change in velocity of particle in the time interval Δt, then- ## Important Notes-

It is important to note the following points-

### Note-01:

• Acceleration is always in the direction of increasing velocity.
• Change in velocity = Final velocity – Initial velocity

### Note-02:

It is worth remembering the following relation- ### Note-03:

We know, Average Velocity

= Total displacement / Total time taken

But if the motion is uniformly accelerated, then average velocity can also be written as- ### Note-04:

• Negative acceleration is called as Retardation or Deceleration.
• It is responsible for decreasing the velocity of a particle.

To gain better understanding about Acceleration,

Watch this Video Lecture

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