# Displacement and Velocity

## Key Questions

"Velocity" = (" Change in displacement " or trianglebarx)/( "Change in time " or trianglet )

#### Explanation:

To define the fastness of an motion , we need to find how fast the space coordinates ( position vector ) of a particle relative to a fixed reference point changes with time . It is called as " Velocity ".

Velocity is also defined as the rate of change of displacement .

Velocity is a vector quantity . It depends on both magnitude and direction of the object .

When a particle moves , it's positive vector $\overline{r}$ must change in direction or magnitude or both ,Velocity is defined as the rate of change in direction or magnitude of $\overline{r}$ with respect to time .

It is measured in $m {s}^{-} 1$ , $k m p h$ , $\text{ miles per hour }$ ,etc.

It has dimensional formula - $\left[{M}^{0} {L}^{1} {T}^{-} 1\right]$
or simply - $\left[L {T}^{-} 1\right]$

• Velocity has direction, whereas speed has only magnitude (size).

Speed is a scalar quantity so it only has magnitude (size).

$S p e e d = \left(\text{distance")/("time}\right)$

Velocity is a vector quantity so it has magnitude and direction.

$V e l o c i t y = \left(\text{displacement")/("time}\right)$

In practical terms this means that velocity is always measured with reference to a specific position. For example, it might be where the observer is standing. In that case a football moving away from the observer would have a positive velocity, but a football moving towards the observer would have a negative velocity.

In more complex situations an angle can be used to define the direction of the velocity vector. In those cases trigonometry and possibly the Pythagoras theorem are used for solutions.

A straight line path joining the initial and final positions of the body irrespective of the fact that this straight line path is actually travelled by the body or not is known as displacement.

#### Explanation:

Displacement is a vector quantity because it has both magnitude and direction which means that change in direction, change in magnitude or change in both magnitude and direction will change the value of displacement.

• Being a vector quantity the value of displacement can be positive when the direction of initial and final positions are the same, negative when the directions of both initial and final positions are opposite and zero when the initial position of the body coincides with the final positions of the body.
• It is always a straight line path and can never be a curve, zig- zag or some irregular path joining the initial and final positions of the body that is why it is also defined as the shortest path length travelled by the body joining the initial and final positions of the body.
• Also, it doesn't matters that the body is actually covering that straight line path or not. If it is a straight line joining he initial and final positions of the body it will always be the displacement of the body.