### Speed

Speed is defined as the **rate of change** in **distance**. It is a measure of **how fast the distance change** in a movement.

Speed is a **scalar** quantity.

When a car travels on a road, the average speed of the car can be calculated by using the following calculation:

Average speed \(=\frac{\text { distance moved }}{\text { time taken }} \quad\)

Or, in symbols:

**\(\quad v=\frac{s}{t}\)**

If distance is measured in metres \(( m )\) and time in seconds \(( s )\), the unit of the speed is measured in metres per second \(( m / s ) ). m/s (metre per second) is the** SI unit of speed**.

For example: if a car moves \(60 m\) in \(5 s\), its average speed is \(12 m / s\).

However, because a car’s speed varies on most journeys, the actual speed at any one time is usually different from the average speed.

In order to **determine an actual speed**, we need to determine how far the car travels in the **shortest time** possible.

For example, if a car moves \(0.35\) metres in \(0.01 s\) :

\[

\text { speed }=\frac{0.35 m }{0.01 s }=35 m/s

\]

### Velocity

Velocity is defined as the **rate of displacement change**. It is the measure of **how fast** the **displacement changes** for a moving object.

Velocity is a **vector** quantity. It has both magnitude and direction.

Velocity tells the speed of something and its direction of travel. The **speed** is the** magnitude** of velocity.

For example, a cyclist might have a velocity of \(20 m / s\) due east. On paper, this velocity can be shown using an arrow:

#### Positive or Negative Sign of Velocity

In velocity, the** positive/negative sign** indicates **direction**.

You can take any direction as positive and the opposite as negative.

For motion in a straight line, you can use \(+\) or \(-\) to indicate direction. Usually, we take the motion to the right as positive and hence the move to the left as negative.

For example:

\(+5 m / s\) (velocity of \(5 m / s\) to the right \()\)

\(-5 m / s\) (velocity of \(5 m / s\) to the left \()\)

### Comparing Speed and Velocity

\[

\begin{array}{|l|l|l|}

\hline & \text { Speed } & \text { Velocity } \\

\hline \text { Definition } & \begin{array}{l}

\text { Speed is the rate of } \\

\text { change in distance. }

\end{array} & \begin{array}{l}

\text { Velocity is the rate of } \\

\text { change in displacement. }

\end{array} \\

\hline \text { SI unit } & \text { ms }^{-1} & \text { ms }^{-1} \\

\hline \text { Quantity } & \text { Scalar } & \text { Vector } \\

\hline \text { Equation } & \begin{array}{c}

\text { Average speed } \\

=\frac{\text { Total Distance }}{\text { Total Time }}

\end{array} & \begin{array}{r}

\text { Velocity= } \frac{\text { Displacement }}{\text { Total Time }} \\

\text { or } v=\frac{s}{t}

\end{array} \\

\hline

\end{array}

\]