Velocity Formula: Definition with Examples

Velocity formula: Velocity is a concept you encounter frequently in everyday life. While traveling by car, when you estimate the time to reach your destination and think about how to speed up, you consider the velocity of your vehicle. Again, the velocity of the bowling actions amazed you during the cricket match. 

So, velocity is all around us. But to use it effectively, you must understand how to calculate and apply the velocity formula in real-life scenarios. This blog explains velocity formulas through examples to help you master the concept 

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What is Velocity?

Velocity is the rate of change of position of an object in a particular direction over a time frame. For example, when we say a car is moving at 60 km/hour toward the north, it means the car undergoes a displacement of 60 km from its original position in 1 hour in the north direction. 

What is the Formula of Velocity?

We often need to calculate the velocity of something moving along a straight line with a uniform velocity. The basic formula of velocity, in this case, is given below:

Velocity (v) = Displacement (d)/Time (t)

Therefore, Velocity is always expressed in the unit of displacement/time. The SI unit of Velocity is meters per second (m/s). 

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Difference Between Speed and Velocity Formula

Speed and Velocity indicate the rate of change in position concerning time, but there are some basic differences between the two parameters.

Speed: 

Speed is a scalar quantity that has magnitude but no direction. It refers to the distance covered in unit time, in any direction.

The speed formula is:

Speed = Distance /Time

Velocity:

Velocity is a vector quantity because it has both magnitude and direction. It refers to the displacement rate along the straight-line distance from the initial to the final position.

The velocity formula is:

Velocity = Displacement/Tim

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Speed and Velocity Example

Suppose a person covers a distance of 300 m from point A to point B and returns to point A. The total Time taken is 20 minutes.

In this case,

Distance = 300 m + 300 m = 600 m

Displacement = 0 meters because the initial and final positions are the same.

Speed = 600 / 20 = 30 m/min

Velocity = 0 / 20 = 0 m/min

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Constant Velocity vs Acceleration

A constant or uniform velocity is when the object covers an equal distance along a straight line in an equal interval of Time. For example, if the object displaces by 5 m every 3 min interval, it is said to be in constant Velocity. 

This means its Velocity is the same at every point of movement.

Again, the object may cover the first 5m in 3 min and the second 5 m in 2 min, then the rate of displacement changes, and the object is said to be in acceleration, which means the Velocity is not uniform.

Average Velocity Formula

The concept of average Velocity comes into practice when the Velocity is not constant. In this case, we calculate the average Velocity using the following formula:

Average Velocity = Total Displacement/Total Time taken

If the initial Velocity and final Velocity are known, then the average Velocity can be calculated using the following formula:

Average Velocity = (Initial Velocity + Final Velocity)/2 

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Types of Velocity Equations

Velocity equations denote the rate of change of displacement depending on the type of motion. The different velocity equations used in physics are as follows:

Final Velocity Equation

This equation gives the final Velocity after a specific time when an object moves with a uniform acceleration.

The equation is as follows:

v = u + at

Where:

• v = final Velocity

• u = Initial Velocity

• a = acceleration

• t = time

Velocity Equation Without Time

This equation helps to determine speed when Time is unknown, but displacement is known.

The equation is as follows:

v²=u²+2as

Where:

• s = displacement

• v = final Velocity

• u = Initial Velocity

• a = acceleration

Velocity Formula Solved Examples

Example 1: Basic Velocity

Question: A person walks 60 meters north in 15 seconds. What is their velocity?

Solution:

• Displacement = 60 meters

• Time = 15 seconds

Therefore, velocity = displacement/time = 60/15 = 4 m/s.

Example 2: Average Velocity

Question: A car travels 80 km east in 2 hours, then 50 km west in 1 hour. What is the average Velocity?

Solution:

• Total displacement = 80 – 50 = 30 km in the east direction from the original position

• Total time taken = 2 + 1 = 3 hours

Therefore, average Velocity = Total displacement/Total time

= 30/3

= 10 km/hour

Example 3: Final Velocity Using Acceleration

Question: A car starts from rest and accelerates at 5 m/s². What is its final Velocity after 10 seconds?

Solution:

We will use the formula to get the final Velocity:

v=u + at

Here, u = 0 (starts from rest), a = 5 m/s², and t = 10 seconds.

Therefore, final velocity v = 0 + 5 x 10 = 50 m/s.

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Graphical Representation of Velocity

In physics, graphs are often used to explain the concept of Velocity by showing how an object changes position and speed over Time. The most common types of graphs are as follows:

Displacement vs. Time Graph

It is a graphical representation of the different positions of an object at different points in time. It shows how the displacement changes with Time, which indicates the Velocity.

The graph shows how displacement increases with time. The straight-line nature of the graph indicates a constant velocity, which means equal displacement in equal time intervals.

Velocity vs. Time Graph

When the object moves at variable speed, the time vs. velocity graph shows how the velocity changes over time.

The above graph shows how the velocity changes with time. The slope of this graph represents the acceleration and the area under the graph represents the displacement. 

Velocity is a core concept in physics and essential for understanding the motion of objects. Understanding the basic concepts of velocity and how to apply the velocity formula and the right velocity equation will help you handle motion-related problems much more easily and quickly.

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