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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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.

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

V = $ \lim_{\Delta t \to 0 }$ $\frac {\Delta x}{\Delta t}$ = $\frac {dx}{dt}$ m /sec

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Mathematically, it can be defined as:

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 (V_{av}) is:

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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 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

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

$\omega$ = angular velocity of the object

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.

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In case of uniform velocity, the object should not change its direction and it should travel with the constant speed at all time.

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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