Speed and Velocity


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 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

\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} \\

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