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## What is Speed?

The time rate of change of distance is called speed. Speed defines “How fast an object is moving?”. Speed is a scalar quantity. It has magnitude only. Speed is not defined by the direction of the motion. The dimension of speed is `\([LT\text{-}1]\)`.

## Speed Formula

Consider a body is moving along a path ‘L’. It covers a distance 'S' in time interval 't’. Then the speed ‘R' of the moving object is given by the formula

`\(R = \dfrac{S}{t}\)`

*Where:*

**R-**is the speed**S-**is the distance travelled**t-**is the time taken to travel distance S.

## Speed Unit** **

SI unit of speed is meter per second (`\(ms\text{-}1\)`), most commonly used to measure the speed of animals, humans and free-falling objects. Other units are kilometer per hour (written in abbreviated version as `\(kmh\text{-}1\)`) and miles per hour (the symbol is \(mph\text{-}1\)). These are derived units of speed. Speedometers of vehicles mostly use \(kmh\text{-}1\) to show the speed. Another unit of speed is knotted, used in measuring the speed of boats and ships.

We can convert one unit of speed to others by multiplying with a suitable conversation factor. For example, if we want to convert `\(18ms\text{-}1\)` into kilometre per hour, a suitable factor to multiply will be `\(3600 seconds/1000 meters\)`.

**Result:**

`\(18 \times 3600 = 64,800 mh\text{-}1\)`

`\(\dfrac{64,800}{1000} = 648 kmh\text{-}1\)`

## Average speed

The ratio of the total distance to the time taken to travel the total distance is called average speed. It is an estimated rate at which the motion takes place. The formula of average speed is

`\(\text{Average speed} = \dfrac{\text{total distance traveled}}{\text{total time taken}}\)`

## Instantaneous speed:

speed of a body at a particular instant of time, when ∆t following the time t approaches to zero. The formula of instantaneous speed is

`\(\text{Instantaneous speed = limit as }\Delta t \text{approaches to zero} \Big(\dfrac{\Delta S}{\Delta t}\Big)\)`

## What is Velocity?

The time rate of change of displacement is called velocity. Velocity is a vector quantity. It is defined completely by magnitude and direction. The dimension of velocity is `\([ LT -2 ]\)`

### Velocity Unit:

As the formula for speed and velocity are the same, units of velocity and speed are also the same.

## Velocity Formula

speed is also known as the magnitude of velocity. The direction itself does not has any unit. So velocity and speed have units in common. Velocity is represented by small bold v (v). Formula to calculate velocity is

`\(\text{Velocity v} = \dfrac{\text{displacement d}}{ \text{Time t}}\)`

## Velocity calculator

Use our velocity calculator to measure velocity. It is completely functional and easy to use. Enter distance and time in meters and seconds respectively and calculate velocity easily.

## How to calculate average velocity?

Consider a body travel a distance d in time t then the average velocity of the body is given by the formula

`\(V_{av} = \dfrac{d}{t}\)`

**Where:**

**V**is the average velocity_{av-}**d-**is displacement**t-**is time.

One cannot tell about the motion between two points using average velocity. For example, if a squash ball is hit on a wall, it comes back after striking the wall. Initial and final positions are the same, so the average velocity is zero. But we know that the ball has covered some distance. Hence, average velocity cannot tell about the motion. This problem is sorted out using instantaneous velocity.

## Instantaneous velocity

The concept of instantaneous velocity can be understood with the help of the following example. Let a body be moving along path DFG in the Cartesian plane. At any instant t, the body is a point D. The position of the body is represented by r1 (position vector). Let the body be at point F, after a small interval of time (∆t) following the time t. This position of the body is represented by r2. Displacement of the body in travelling from D to F is

`\(\Delta d = r2 - r1\)`

**Please Note:**

∆ means a small change.

If we bring F close to D by making ∆t smaller and smaller, ∆d it will also become smaller relatively and a point a will reach when** **∆t will become almost zero but will not completely disappear. Velocity at this particular instant is called instantaneous velocity.

Instantaneous velocity is expressed in mathematical form as

`\(V_{ins} = \text{limit as} \Delta t \text{approaches to zero} \Big(\dfrac{\Delta d}{\Delta t}\Big)\)`

If the instantaneous velocity remains constant, the velocity of a body remains constant.

## What is Linear velocity?

When a body is moving along a straight path, the velocity of the body is linear.

## What is Angular velocity?

when a body is moving in a circle, it’s moving with angular velocity and it is directed towards the centre of the circle.

## Real-life examples

we use the concept of velocity in daily life a lot. Following are some examples.

- When one is driving a car from the office back home. There must be some speed (magnitude of velocity) with which the car is being driven and of course a direction also. Let the car be moving with 140kmh-1 in the south. Speed and velocity both are 140kmh-1. Now if you reverse your car after stopping for a while at a speed of 20kmh-1. Your velocity will be -20kmh-1.

- The minute hand of a watch moves with a velocity of 0.0017 rads-1.

- Satellites are sent into an orbit around the earth while keeping in view ‘escape velocity' (11.2 Kms-1).

- A ball thrown upward goes up with a decreasing velocity while comes back with increasing velocity. Average velocity is zero.

- In the world of cricket, a Bowler always has a bowling speed or velocity with which it bowls the ball. For example, bowling speed of Wahab Riaz, a Pakistani bowler, is 144.8kmh-1.

## What is Acceleration?

If the velocity of the body does not remain constant, the body is said to possess acceleration. The time rate of change of velocity is called acceleration.

Acceleration is also a vector quantity. Acceleration may be produced by a change, whether in magnitude or direction of velocity. The dimension of acceleration is [LT-2]. It is represented by** “a”.**

### Acceleration Unit:

Unit of acceleration is ms-2 and is read as a meter per second squared. Some other common units are Kmh-2, mph-2.

## Acceleration Formula

Consider a body has a velocity v1 at any instant t1 and has velocity v2 at another instant t2. This change in velocity in time `∆t` is called average acceleration.

`\(a_{av} = \dfrac{\Delta v}{\Delta t}\)`

The direction of acceleration is the same as velocity.

## Instantaneous acceleration

Acceleration at an instant ∆t, which when following the time interval **t** approaches to **zero**, is called instantaneous acceleration.

Mathematical form is

`\(a_{ins} = \text{limit as} \Delta t \text{approaches to zero}\Big(\dfrac{\Delta d}{\Delta t}\Big)\)`

When a body moves with increasing velocity, then it is said to possess positive acceleration. When a body moves with decreasing velocity, then it is said to possess negative acceleration and this negative acceleration is called Retardation. If a body changes its velocity equally in equal intervals of time, then acceleration produced is said to be constant. Instantaneous acceleration and average acceleration also become equal at constant acceleration.