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# Speed|Definition & Meaning

## Definition

Speed defines the **rate** at which an object is traveling. An object covers a **distance** at some **time** with a certain speed. The speed determines how **fast** an object moves, given that it covers some **distance**. An object at **rest** has no **speed.**

**Figure 1** shows a car moving at a certain **speed** from the **initial** point to the **final** point.

## Speed’s Mathematical Formula

The time **rate** of change of **distance** covered by an object is known as speed. It can be expressed **mathematically** as follows:

**Speed = Distance/Time**

**s = d/t**

Where **s** is the **speed** of the object covering a** distance d** per **time t**, speed is also denoted by **v** sometimes as it is the magnitude of **velocity. ****Distance** and **time** play an important role in the discussion of **speed.**

### Distance

Distance is a **quantity** that determines how much of a **length** an object has covered. It is denoted by “**S**” or “**d**”. It is measured in **meters(m)** in **SI** and also measured in kilometers(**km**).

**Kilometers** and **meters** are related as follows:

**1 km** = 1000 m

Similarly,

**1 m** = 1/1000 km = 0.001 km

A distance always has a **starting** point and a **finishing** point. It does not have a direction, hence is a **scalar** quantity. It is **zero** when the object is at **rest.**

**Figure 2** shows two balls, one at **rest** and the other covering a **distance** from **A** to **B**.

### Time

Time is defined as the ongoing **independent** quantity that produces a **change** in conditions. **Einstein** called it **relative** to some frame of reference.

It is a passing **fundamental** quantity through which the change in all other quantities can be noticed.

Its System International unit is **seconds(s) **and is a **scalar** quantity.

It can also be measured in **hours,** minutes, days, months, years, etc. For **speed,** the time taken is usually in **seconds** and **hours.**

As:

1 hr = 60 min

1 min = 60 sec

So the relation between an **hour** and a **second** is:

1 h = 60 × 60 = 3600 s

Hour and seconds are also abbreviated as “**hr**” and “**sec**” respectively.

## Units of Speed

The commonly used **units** of speed are as follows:

### Meters per Second

The unit used for **slower** speeds is meters per second. It is also used when a **small** amount of **distance** is covered.

It is written as “**m/s**” and means that an object covers this many **meters** in one **second.**

For example, **30 m/s** speed refers to an object covering **30 meters** every **second** of the journey.

### Kilometers per Hour

The **second** unit of speed is kilometers per hour. It is abbreviated as “**km/h**”.

The distance covered by **vehicles** on roads is in **kilometers** and it requires a lot of seconds to cover a few kilometers. That is why the unit **hour** is used with the kilometer.

It is defined as how many kilometers an object **travels** in an hour. For example, the speed of **100 km/h** refers to covering **100 km** in one **hour.**

## Uniform and Non-uniform Speed

When an object covers the **same** amount of **distance per time interval**, its speed is **uniform**.

**Non-uniform** speed refers to an object covering an **unequal** distance in each time interval. **Figure 3** shows the illustration of **uniform** and **non-uniform** speed.

## Velocity

The speed with a **direction** is known as velocity. It has the same **magnitude** as **speed,** but it is a vector quantity.

**Velocity** is denoted by $\overrightarrow{v}$ and **speed** by v. The **formula** for velocity is the same as speed.

The **direction** is specified by using the words north, south, east, and west.

## Acceleration

The change in **velocity** per unit of time is called acceleration. An object **accelerates** when it **changes** its velocity. It means that either or both its magnitude (**speed**) or **direction** can change.

The mathematical **formula** for **acceleration a** is:

a = v/t

It is measured in meters per second squared (**$ms^{-2}$**).

## Speed-Time Graph

The speed-time graph shows the **acceleration** produced in an object. **Time** is the **independent** quantity and is taken on the x-axis.

The change in **speed** depends upon time; hence it is the **dependent** quantity and is taken on the y-axis. Two main **cases** arise while discussing the change in speed.

### Case 1

When an object is moving with a **constant speed,** no acceleration is produced in the object.

**Figure 4** shows the speed-time graph for an object moving with constant speed.

The graph shows a straight **horizontal line,** so the acceleration is **zero.**

### Case 2

If an object moves with a **uniform speed,** the object accelerates with uniform **acceleration.**

**Figure** **5** shows the graph for uniform change in **speed** in equal time intervals.

The rising **slope** shows that a **positive** acceleration is produced.

## Speed of Light

The speed of light denoted by **c** is a universal constant and has an essential role in **physics.**

It is defined as the speed of **light** waves when traveling through space or a **vacuum**. Its value is **299,792,458** **m/s** or approximately **300,000 km/s**.

## Solved Example of Speed Calculation

A **car** covers a **150 km** distance in **5 hours.** At what **speed** is the car moving? Also, find the speed in meters per second.

### Solution

The distance “**d**” value is **150 km,** and the time “**t**” given is **5 hours**. The formula for speed is given:

s = d/t

Putting the **values** in the above equation gives:

s = 150 km / 5 h

**s = 30 km/h**

So, the **speed** of the truck is **30 km/h**. To convert it into meters per second, divide by 3600 and multiply by 1000 as follows:

s = 30(1000)/3600 m/s

**s = 8.33 m/s**

The **speed** of the truck in meters per second is **8.33 m/s**.

*All the images are created using GeoGebra.*