To understand this topic, one must be clear about the concepts of terms like Velocity, Acceleration, Speed and Displacement. The term ‘Speed’ and ‘Velocity’ are often inter-changed although erroneously. The important difference between Speed and Velocity is :-

Speed is a **Scalar quantity** (a term defined by magnitude alone). Whereas, Velocity is a **Vector quantity** (a term described both by magnitude and direction). Speed refers to how fast an object is moving. Where as, Velocity refers to the rate at which an object is changing its position.

The differentiation between Distance and Displacement would also be useful as we would use these in the mathematical and word definitions of Average Velocity. Distance is a Scalar quantity referring to how much ground a given object has covered. Where as, Displacement is a Vector quantity referring to how distant/close an object is from a given point.

**Average Velocity:**

The Average Velocity of an object is defined as its total Displacement divided by total Time taken.

In other words, Average Velocity is the ratio between Displacement of an object from point1 to point2 and the Time taken by the object to make the displacement. Average Velocity is a Vector quantity since its determined by both the magnitude and distance covered by an object. Average Velocity is generally defined by SI units like Meters/second, Miles/hour(mph), Kilometre/hour (km/hr) etc.

**How to Calculate Average Velocity:**

To calculate the Average Velocity we divide the total Displacement by the total time taken. Hence, Average velocity = (change in position) / (change in time)

- In simple words, Average Velocity = Object position divided by Time = Displacement divided by Time

It is important to make a distinction between Average Speed and Average Velocity. As explained above Speed is a Scalar quantity and Velocity is a Vector quantity.

- Average Speed = Distance travelled divided by Total time of Travel

Let’s take an example to clarify the difference between Average Speed and Average Velocity:

For instance, let’s say if a jeep is said to be moving at the rate of 80 miles per hour (128.75 km/h), then we are describing the Speed of the object. If the Jeep is said to be travelling at 80 miles (ca. 129 km)/hour in the South direction then we are describing its Velocity.

**Solved Questions and Answers**

Now, let’s solve a question!

Q) If a jeep is traveling toward the South at a speed of 120 km/hr for 5 hours then changes its course to West at the speed of 60 km/one hour. Calculate Average speed and Average Velocity.

So, Total distance travelled = 120+60 km=180 km

Displacement = 120 km-60 km= 60 km to East

Average Speed= Distance/ Time taken= 180 km/6hours= 30 km/hr

Average Velocity= Displacement/ Time taken = 6okm/6hr = 10 km/hr

The direction of the Velocity is nothing but the direction in which the object is moving. If the direction of the velocity non-numerical, for example, moving upward or downward, then the Velocity is defined in similar terms. Ex: If an object is moving towards the left, westwards with the speed of 200 miles (321.87 km)/hour, then its Velocity is said to be Leftwards 200 miles (321.87 km)/hour West.

- Some examples below will clearly show you how to calculate Average Velocity when different variables are used in the question: –

1. A bike travels 2 km in Northward direction and then moves in the South direction for another 4 km. If the whole of biking takes a total of 15 minutes, find the Bike’s Average Velocity during the entire journey.

Since the journey was made in two parts, after 15 minutes, the final displacement is 2 km south of the starting point. Therefore, the Average velocity is explained as-

2. If an athlete finishes a 100 m sprint in a total of 9.8 seconds, Find the Average Velocity at which the athlete sprinted.

A train passes a subway at 12kmh-1 An hour later the same train passes another station. If the train was repeatedly accelerating at the velocity 48kmh-1 when passing the second subway, what is the Average velocity of the train within the hour?

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