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# Velocity

• Last Updated : 12 Sep, 2022

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 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. Let’s learn more about velocity, the unit of velocity, different formulas of velocity difference between speed and velocity, problems on velocity, and many more in this article!

## What is Velocity?

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).

### Initial and Final Velocity

Initial Velocity is the velocity when the motion of the object started. In simple words, the velocity at 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.

## 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 Formulas

The general formula used to calculate velocity is stated as,

Velocity = Displacement / Time

or

v = s / t

where,

v is the velocity of the object,

s is the Displacement of the object and

t is the time taken

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 (xi) and the final position (xf) of an object along with the time interval are given, then the velocity can be calculated as,

Velocity = Final Position – Initial Position / Time = Change in the Position / Time

or

v = xf – xi / t = Δx / t

where,

xf and xi are the final and initial velocities of the object and

Δx is the change in the position.

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,

Final Velocity = Initial Velocity + Acceleration × Time Taken

or

v = u + at

where

v is the final velocity,

u is the initial velocity,

a is the acceleration and

t is the time taken by the object.

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

Initial Velocity = Final Velocity – Acceleration × Time Taken

or

u = v – at

where

v is the final velocity,

u is the initial velocity,

a is the acceleration and

t is the time taken by the object.

Angular Velocity = Angular Displacement / Time Taken

or

ω = θ / t

where,

ω is the Angular Velocity,

θ is the Angular Displacement and

t is the time taken by the object in the circular motion.

• 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,

Escape Velocity = √2 × Gravitational constant × Mass of the object escaped / Distance from the center of the mass

or

ve = √2Gm/ r

where,

ve 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.

## 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.

## Summary for Velocity Formulas

1. v = s / t
2. v = xf – xi / t = Δx / t
3. v = u + at
4. u = v – at
5. ω = θ / t
6. ve = √2Gm/ r

## Solved Examples based on Velocity Formulas

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

Solution:

Given that,

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 that,

Initial position, xi = 0 m,

Final position, xf = 40 m, and

Time taken, t = 10 s.

Since,

v = xf – xi / 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 that,

Acceleration, a = 20 ms-2,

Initial velocity, u = 0 m/s, and

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 that,

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

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 that,

Acceleration, a = 2 ms-2,

Initial velocity, v = 20 m/s, and

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:

The mass of the earth, m = 6 × 1024 kg,

The 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

The value of gravitational constant, G = 6.67 × 10−11 Nm2/kg2.

Since, the escape velocity is defined as,

ve = √2Gm/ r

Therefore,

ve = √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.

## FAQs on Velocity Formulas

Question 1: What is Instantaneous speed?

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

Question 2: 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).

Question 3: Can Initial Velocity be Zero?