What is Velocity?

Velocity is an essential concept in physics, which measures the rate of change of an object’s position with respect to time. When the speed of an object is measured in a specific direction, then it is termed Velocity. Also, the time-rate change of displacement is known as velocity. Both speed and velocity are quite similar to each other. But exhibits an important difference in that velocity is a vector quantity that has both magnitude and direction. And speed is a scalar quantity that has magnitude only. Thus, Velocity is a measure of how much time a body takes to reach a destination with direction.

For example, when two objects are traveling in the same direction, then it is easier to tell the faster. But, if the direction of motion of the two objects is in the opposite direction, then it is difficult to identify the fastest. In such situations, the concept of velocity is essential.

Velocity Definition

Velocity is defined as  the rate of change of the position of the object with respect to a frame of reference and time

Velocity is a vector measure of the speed and direction of movement. Simply put, velocity is the pace at which something moves in a particular direction. The speed of a car going north on a major highway and the speed of a rocket bursting into space may both be measured using speed. As one may anticipate, the scalar size (total value) of vector velocity represents the speed of movement. In terms of computations, speed is the first exit of a place in terms of time. Speed can be calculated using a simple formula using measurement, distance, and time.

Unit of Velocity

• The SI unit for velocity is m/s (meters per second).
• At the same time, velocity can be expressed in any unit of distance. Other units include miles per hour (mph), kilometers per hour (kph), and kilometers per second (km/s). 

Types of Velocity

There can be various types of velocities for any object, some of these types are as follows:

• Uniform Velocity 
• Non-Uniform Velocity
• Instantaneous Velocity
• Average Velocity

Let’s understand these velocities as follows:

Uniform Velocity 

When any object travels equal displacements in equal times then its velocity is called uniform velocity. A train traveling at a constant speed of 80 kilometers per hour (km/h) for 2 hours will cover a distance of 160 kilometers (km), then the velocity of a train traveling at 80 kilometers per hour is an example of Uniform Velocity.

Non-Uniform Velocity

When any object travels unequal displacements in equal time intervals then its velocity is called non-uniform velocity. For example, a car traveling at 30 km/h in a crowded street, then accelerating to 80 km/h on a highway, and then slowing down to 50 km/h in a suburban area, then the car is said to be having non-uniform velocity.

Instantaneous Velocity

Velocity at a certain moment or over a very short period of time for any object is called instantaneous velocity. Let’s consider a car traveling at a constant speed of 100 km/h on a highway, and the driver looking at the speedometer to see its velocity is an example of instantaneous velocity at that moment.

Average Velocity

For a moving object with some velocity, the total distance traveled per unit of time is called the average velocity of that object. i.e.,

Average Velocity = Total Displacement Travelled / Total Time Taken

Let’s consider, a person walks a distance of 4 km in 1 hour, then walks another 2 km in 30 minutes. The average velocity for the whole trip is 8 kilometers per hour (km/h).

Initial and Final Velocity

Initial Velocity is the velocity when the motion of the object started. In simple words, the velocity at a time interval t = 0 s is called the Initial velocity. It is represented by the symbol u. The SI unit is similar to that of the velocity i.e. m/s.

Final Velocity is the velocity attained by the object when it reaches maximum acceleration. In simple words, the velocity gained by the object at a certain time interval is called the Final velocity. It is represented by the symbol v. The SI unit of both initial and final velocities are the same i.e. m/s.

How to find the final velocity?

Follow the following steps to find the Final velocity of the object.

Step 1: The object’s initial velocity can be calculated by dividing the total distance traveled by the amount of time it took the object to travel that distance. In the formula V = d/t, V is the speed, d is the distance, and t is the time.

Step 2: By dividing the mass of the object by its force, then multiplying the result by the acceleration’s time, you can determine its acceleration.

Step 3: To get the final velocity, add the amounts from Steps 1 and 2.

Constant Velocity

The constant velocity of an object is gained when it has a constant speed in a constant direction. Here the constant direction restricts the object to move in a linear or straight path. Therefore, the constant velocity is then termed as the motion of the object in a straight line at a constant speed.

One of the simplest forms of motion is when the object moves with a constant velocity. Such a constant motion can be witnessed whenever an object slides over a horizontal surface.

However, a bicycle moving at a constant of 50 km/h in a circular path has a constant speed but does not have a constant velocity because its direction changes following the circular path.

Velocity Formula

There are different formulas to calculate the velocity of an object using different parameters under various conditions. Here are some of the major formulas used to calculate different velocities as-

When the initial (x_i) and the final position (x_f) of an object along with the time interval are given, then the velocity can be calculated as,

 

Now, according to the Equations of motion, the velocity can be evaluated,

• When initial velocity, acceleration, and time are given then the final velocity is given as,

 

where

• v is the final velocity, 
• u is the initial velocity, 
• a is the acceleration and 
• t is the time taken by the object.

Difference between Speed and Velocity

Speed and velocity are terms that are often used in a similar manner so are a little confusing for most of us. But, practically there is a significant difference between both of the terms. 

The term Speed is used to express how fast a body is moving. However, velocity not only expresses its speed but also briefs us about the direction in which the body is moving.

Hence, speed is simply defined as the rate of change of the distance traveled by an object in a given time interval. While velocity is defined as the rate of the displacement of an object in a given time interval. This implies that speed is the function of distance and velocity is the function of displacement. And most importantly, speed is said to have magnitude only so is a Scalar quantity, while velocity has both magnitude and direction, it is a vector quantity. Moreover, both quantities have the same units and dimension formulas. 

The difference between Speed and Velocity in tabular form is given as follows:

Speed	Velocity
The rate of change of the distance traveled by an object in a given time interval is called Speed.	Velocity has defined as the rate of the displacement of an object in a given time interval
It is a function of distance only.	While it is a function of displacement only.
Speed is said to have magnitude only so is a Scalar quantity	While velocity has both magnitude and direction, it is a vector quantity.
The speed of an object moving can never be negative	The velocity of a moving object can be zero.
Speed denotes how rapidly the object moves.	While velocity denotes how rapidly the object moves in a direction.

Angular Velocity

When the angular displacement and time taken by the object in a circular motion are given, then the angular velocity is given as,

 

where,

• ω is the Angular Velocity
• θ is the Angular Displacemen
• t is the time taken by the object in the circular motion.

Escape Velocity

When the mass of the object escaped from the Earth’s gravitational pull (with gravitational constant G) is given, then the escape velocity of the object is given as,

where, 

• v_e is the escape velocity, 
• G is the Universal Gravitational constant (= 6.674 × 10^-11 Nm²/kg²), 
• m is the mass of the object escaped and 
• r is the distance from the center of the mass.

Summary for Velocity Formulas

All the different formulas to calculate different velocities are as follows:

• v = s / t
• v = (x_f – x_i)/ t = Δx / t
• v = u + at
• ω = θ / t
• v_e = √2Gm/ r

Also, Check

• Distance and Displacement 
• Acceleration
• Speed and Velocity

Solved Examples on Velocity

Example 1: In one hour, a car may travel 550 km. Calculate its velocity.

Solution:

Given,

• Displacement, s = 550 km = 550 × 10³ m
• Time taken, t = 1 h = 3600 s

Since,

Velocity = Displacement / Time

v = 550 × 10³ / 3600

= 152.77 m/s

Hence, the velocity of the car is 152.77 m/s.

Example 2: A car starts and covers a displacement of 40 m in 10 s. Calculate its velocity. 

Solution:

Given,

• Initial position, x_i = 0 m
• Final position, x_f = 40 m
• Time taken, t = 10 s.

Since,

v = x_f – x_i / t 

Therefore, 

v = (40 m – 0 m) / 10 s

= 4 m/s

Hence, the velocity of the car is 4 m/s.

Example 3: A player hits a football that is initially at rest and attains the acceleration of 20 ms^-2 in time 5 s. Determine the final velocity of the football after t = 5 s.

Solution:

Given,

• Acceleration, a = 20 ms^-2
• Initial velocity, u = 0 m/s
• Time taken, t = 5 s.

Since,

v = u + at

Therefore,

v = 0 m/s + 20 ms^-2 × 5 s

= 100 m/s

Hence, the final velocity of the football after t = 5 s is 100 m/s.

Example 4: Determine the angular velocity of the ball displaced in a circular motion by an angle of 30 radians in 5 s.

Solution:

Given,

• Angular displacement, θ = 30 rad
• Time taken, t = 5 s

Since, the angular velocity is given as:

ω = θ / t

Therefore, 

ω = 30 rad / 5 s

= 6 rad/s 

Hence, the angular speed of the ball is 6 rad/s.

Example 5: A person completes a distance with a final velocity of 20 m/s and acceleration of 2 m/s² in time of 4 s. Calculate its initial velocity.

Solution: 

Given,

• Acceleration, a = 2 ms^-2
• Initial velocity, v = 20 m/s
• Time taken, t = 4 s.

Since, the initial velocity is:

u = v – at

Therefore,

u = 20 m/s – 2 ms^-2 × 4 s

= 12 m/s

Hence, the initial velocity of the person is 12 m/s.

Example 6: What will be the escape velocity of an object from the earth’s surface?

Solution:

• Mass of the earth, m = 6 × 10²⁴ kg,
• Distance of the object from the center of the mass is equals to the radius of the earth, r = 6400 km = 6.4 × 10⁶ m, and
• Value of gravitational constant, G = 6.67 × 10⁻¹¹ Nm²/kg².

Since, the Escape Velocity is defined as,

v_e = √2Gm/ r

Therefore, 

v_e = √2 × 6.67 × 10⁻¹¹ × 6 × 10²⁴ kg / 6.4 × 10⁶ m

= 11200 m/s

= 11.2 km/s

Hence, the escape velocity of an object from the earth’s surface is 11.2 km/s.

Velocity – FAQs

Define Velocity.

When speed of an object is measured in a specific direction, it is called velocity. For example, car moving towards north with speed 40 km/hour, is the example of velocity.

How is Velocity Measured?

Velocity is measured in units of distance per time, typically meters per second (m/s) or kilometers per hour (km/h). It requires both the speed of the object and the direction of its movement.

What is Instantaneous velocity?

Instantaneous velocity is defined as the velocity of an object at a specific instant of time. It is measured in m/s.

What is the Unit of Velocity?

The SI unit for velocity is m/s (meters per second). It is also measured in miles per hour (mph), kilometers per hour (kph), and kilometers per second (km/s).

Can Velocity be zero?

Yes, velocity can be zero. As for an object at rest velocity is always 0.

What are the Types of Velocity?

There are mainly two types of velocity: average velocity and instantaneous velocity. Average velocity is the total displacement divided by the total time taken, while instantaneous velocity is the velocity of an object at a specific moment.

Can Velocity be negative?

Yes, velocity can be negative.

What Factors Affect Velocity?

Factors that can affect velocity include external forces like gravity, friction, and air resistance, as well as the mass of the object if the forces are unbalanced. Changes in any of these factors can cause acceleration, thereby changing the velocity.

How Velocity can be Negative?

Velocity of any object in the opposite direction is always considered with negative sign.

When Velocity is Constant Acceleration is ____.

Acceleration for a constant velocity motion is 0 m/s² as there is no change in the velocity.

How Does Velocity Differ from Speed?

While both velocity and speed measure how fast something is moving, velocity also includes the direction of the movement. This makes it a vector quantity, whereas speed is a scalar quantity, only representing the magnitude of movement.

Is Velocity a Vector Quantity?

Yes, velocity is a vector quantity.

Why Velocity is a Vector Quantity?

As to define velocity of any object we need magnitude as well as direction, therefore velocity is a vector quantity.

What is Average Velocity Formula?

The formula for average velocity is given as 

Average Velocity = Total Displacement Travelled / Total Time Taken

What is the Difference Between Speed and Velocity?

Speed measured in a specific direction is called “velocity,” i.e., if a car is moving at 30 km/h, that is the car’s speed, but if the car is moving at 30 km/h towards the north, that is the car’s velocity.