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# Velocity

Motion is described in terms of time and distance and it signifies that the object is changing its position with respect to a reference point. The well known example is our Earth. As we know our Earth is always in motion, although, for us it seems to be in still position. Speed and velocity, these terms gives us an idea of how slow or how fast a body is moving. Quite a few times, we need to know which one of the two or more objects is moving faster. One can easily tell which amongst all the vehicles, that are moving in the same direction on a same road at any instant of time, is moving faster. But if their direction of motion is opposite to each other, we may not be able to make out which of the vehicle is moving faster. One must have the better understanding of the concepts of velocity to study the motion of any object.

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## What is Velocity?

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Velocity is the measure of the speed of the object in a specific direction. Velocity is a vector quantity so both the magnitude and the direction of the object are required to define the velocity of the object. The speed and velocity of an object are interrelated terms.

To understand it better, consider the following example. An object is moving at, say, 50 m/sec in northwest direction. Here, 50 m/sec is the speed of the object in the northwest direction. And “50 m/sec” is the magnitude of the velocity while the "northwest" is the direction in which the object is moving.

## Velocity Formula

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As we know that velocity is speed of object in a particular direction. It is given that the rate of change of displacement with time. So the equation of velocity is:
V = $\frac{displacement}{time}$.

V = $\lim_{\Delta t \to 0 }$ $\frac {\Delta x}{\Delta t}$ = $\frac {dx}{dt}$ m /sec
Here, $\Delta$x denotes the change in the position or displacement of the object in $\Delta$t time. From this equation, the velocity can be rewritten as the first derivative of the displacement of the object from its initial position.

## Average Velocity

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Average velocity defines the average rate of change of position of an object with respect to time. Therefore, the average velocity depends only on the initial position and the final position of the object and doesn’t depend on the path taken by the object to reach the final position from its initial position.

Mathematically, it can be defined as:

v = $\frac {\Delta x} {\Delta t}$ m / sec = $\frac {x_2 - x_1} {t_2 - t_1}$ m / sec
where,
x2 = final position of the object
x1 = initial position of the object
t2 = time at which object reach the distance d2
t1 = time at which the object starts from the distance d1

Let's take an example to understand the average velocity of an object. An object is moving as shown in table,

 Distance (m) 1 5 6 9 1 Time (Sec) 1 2 3 4 5

From the above table it is clear that the total distance traveled by the object is 22 m in 5sec, so the average Velocity (Vav) is:

Vav = $\frac {22} {5}$ = 4.4 m / sec

## Constant Velocity

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For the constant velocity, an object should have constant speed with constant direction. Constant direction, here means that the object moves in a straight line, as object never changes in a straight line direction.

For example, a bike traveling at the constant speed of 45 mph on a circular track cannot have constant velocity while if the bike travels with same constant speed in a straight line it has constant velocity of 45 mph.

## Initial Velocity

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Initial velocity of an object is the velocity before the application of an external force.

To understand this let’s consider following examples:

1. A football is hit by the player for the first time in the field.
2. A cricket ball is hit by the batsman.

In the example 1, the initial velocity of the football is zero, since it is lying on the floor, while in the example 2 initial velocity of the cricket ball is not zero since bowler delivers this ball with some velocity towards the batsman.

## Final Velocity

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Final velocity is described as the velocity of an object when the distance ends, or it can be defined as the velocity at which when we stop timing. So, final velocity of an object is:
v = $u+a(t_{2}- t_{1})$ m / sec
where,
v = final velocity of the object
u = initial velocity of the object
a = acceleration of the object
t1 = start time
t2 = time at which the object reaches the velocity v

## Linear Velocity

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Velocity can be of two types i.e, linear velocity and angular velocity. The linear velocity defines the motion of the object in the straight line while the angular velocity defines the motion of object in the circular direction.

The linear velocity is denoted by v and angular velocity is denoted by $\omega$ then the relation between both the velocities is:
v = $\omega$r rad / sec
where,
v
= linear velocity of the object
$\omega$ = angular velocity of the object
r = radius of curvature along which object is moving

## Uniform Velocity

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An object is said to be moving with the uniform velocity if it is covering the equal distances in the equal time intervals without changing direction.
In case of uniform velocity, the object should not change its direction and it should travel with the constant speed at all time.

## Velocity and Speed

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Velocity is the change of the position or displacement of an object with time while speed is rate of change of distance with respect to time. However, Velocity is a vector quantity while speed is a scalar quantity. To define a scalar quantity, only magnitude is required while to measure a vector quantity magnitude as well as direction is required.
 More topics in Velocity Uniform Velocity Average Velocity Constant Velocity Initial Velocity Final Velocity Linear velocity
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