What is the difference between deceleration and acceleration?

WHAT YOU INITIALLY NEED TO KNOW?

-Breaking a vector into its components, and basic knowledge of Kinematics.

Now, let's discuss it.

1. Consider a particle travelling in free space while we are observing its nature from the ground frame. 

2. We all believe that acceleration is when speed increasing, and deceleration is when speed is decreasing but is it really true?
3. Let's consider the particle's velocity vector be 'V'. Then let's consider the these 3 fundamental cases which are possible for the acceleration vector 'a'- 

- a is along the velocity vector v 

- a is anti-parallel to velocity vector v 

- a is along a random angle with v 

4. While we can predict that the particle is accelerating in first case and decelerating in second case, what about the third case 

5. In the third case, the particle can be accelerating or decelerating but the deciding factor is the angle between them and 

6. Now you have three sub-cases whether the angle is

-Acute,

-Obtuse, or

-Right Angled

7. 

 

8. Now, as the acceleration vector has a component (shown in Green arrow) in the forward direction in (I), it is accelerating and an anti-parallel component in (II), hence, it is decelerating

There is no such component of acceleration along the velocity vector, so, the particle is not accelerating in (III).

NOTE- 

The above discussion is only valid for that particular instant only, not for a finite time period. 

We need to find out more about the velocity vector and acceleration vector at the next instant to predict whether it is accelerating at that instant or not.

HOW TO DECIDE WHETHER THE ACCELERATION VECTOR IS MAKING WHAT ANGLE WITH VELOCITY VECTOR?

Yeah, you all know. Just take the dot product of the acceleration and velocity vector and find cos(Ɵ)

So, in general for acceleration,

A .V>0

and for deceleration,

A .V<0

and with that I end this post.

THANKS A LOT FOR READING THIS. HOPE YOU LIKE IT!!