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# Speed

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 Sub Topics Everything in this universe moves, even things that appear to be at rest move comparative to the stars and sun. When we discuss the motion of something, we describe the motion related to something else. In this section we will learn more about speed.

## Formula to Determine Speed

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Before the time of Galileo, people described moving things as simply “fast”or “slow”. Such description were vague. Galileo is the first one who measured speed by considering the distance covered and the time it takes.
The speed is defined as the distance covered per unit time.
$Speed$ = $\frac{Distance}{Time}$

A car covers 60 meters in a time of 2 seconds, has a speed of 30 meter per second.

## Unit of Speed

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The unit of speed is m/s or km/h, same as that of velocity, but it is a scalar quantity because it dose not have a direction.
Speed is independent of the direction of motion – it has no direction. It is therefore a scalar quantity.

## Speed Time Graph

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1. When speed remains constant:

Since the speed of a body is constant the speed does not change with time, hence there is no acceleration.

2. When speed changes at an uniform rate:

When the speed of a body changes at uniform rate, its speed changes by equal amounts in equal intervals of time.

3. When the initial speed of the body is not zero:

The graph given below is speed-time graph with initial speed equal to OB.

4. When speed changes at a non-uniform rate:

When the speed changes at a non uniform rate, then the speed-time graph of the body is a curved line. The distance traveled by the body is given by the area between the speed-time curve and the time axis.

## Average Speed

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Many times when a body covers distances by different speeds, we use another term called 'average speed' in this case which is defined as follows:

$Average\ speed$ = $\frac{Total\ distance\ covered}{Total\ time\ taken}$

When a body is in uniform motion its speed and average speed are the same.

## Instantaneous Speed

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Things in motion often have variation in speed. A bus, for example, may travel along a street at 40 km/h. This dose not necessarily mean that the bus is traveling at a uniform rate. The bus would be speeding up or slowing down as it passes the road sign. Instantaneous speed, the speed of bus at any instant. We define the instantaneous speed, to be this limiting value:

Instantaneous speed = $\lim_{\Delta t \to 0} \frac{\Delta d}{\Delta t}$

## Constant Speed

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Constant speed means steady speed. Something with constant speed doesn't speed up or slow down. For example, we all traveled in some form of transport- car, bus, bike etc. Therefore everyone might have some idea of what constant speed is. It is nothing but keeping the speedometer at constant value. When speed is constant one can find the distance traveled during any period of time.

## Angular Speed

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The rotational speed is the speed of the object when the object is moving in a circular motion and the motion is called the circular or rotational or the angular motion. As we know every object which changes its position with time gains a speed for a while in the amount of time in which it changes its position. The object which changes its position on a circle such that the object remains on the circle but with some specific speed and this speed is called the rotational speed of the object.

## Speed Examples

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The following are the example for speed.

### Solved Examples

Question 1: John rides his bicycle and covers a distance of $200 m$  in $40$ seconds. Calculate speed in m/s and km/h.
Solution:

Given,
$Time$  = $40 s$
Distance = $200 m$

We have the formula,

$Speed$ = $\frac{Distance}{Time}$

$Speed$ = $\frac{200}{40}$ = $5$ m/s

We know that to convert from m/s into km/h we have to multiply by 18/5, so

$Speed$ = $5$ m/s = 5 $\times$ $\frac{18}{5}$ = $18$ km/h.

Question 2: A car travels $40$ km at a uniform speed of $50$ km/h and the next $40$ km at a uniform speed of $30$ km/h. Find its average speed.

Solution:

$Average\ speed$ = $\frac{Total\ distance\ covered}{Total\ time\ taken}$

Total distance covered = $40$ km + $40$ km

= $80$ km

As we know that,

$Time$ = $\frac{Distance}{speed}$

Time taken to move first $40$ km = $\frac{40}{50}$ = $0.8$ h

Time taken to move next $40$ km = $\frac{40}{30}$ = $1.333$ h

The total time taken = $0.8 +1.333$

= $2.133$ h

Average speed = $\frac{80}{2.133}$ = $37.505$ km/h