Dimensional Formula Of Velocity

When studying kinetics, it is important to know about scalar and vector quantities. A quantity that possesses a specific magnitude but to a specific direction is called a scalar quantity, whereas a quantity that possesses a particular magnitude and direction as well is called a vector. One such important vector quantity is velocity which we will explain here further.

Often speed is confused with velocity, but both are different properties and quantities. Speed is a scalar entity, whereas velocity is a vector entity. This is because speed is referred to as “how fast an object is moving” here; no information about the direction is required. In contrast, velocity refers to the measurement of both rate and direction of the motion of an object.

What is velocity?

Velocity is described as the measurement of the rate at which an object is changing its position in a specific direction.

For example: if we have to explain velocity with an example, imagine a car is moving 5 kilometres north and coming back to the position from where it started its journey. It is doing the same thing five times; even though this whole act seems like a stupid thing to do but this is resulting in zero velocity. Since the car is coming back to its original position, ultimately, the total journey or the distance covered by it is not possible to be counted as it is always returning to its original position, so the velocity is zero.

Initial and final velocity

When you are counting the velocity of an object, it is extremely important to know what is the velocity when the object started its journey and what was the velocity when it completed the journey. When solving problems with velocity, if the entire velocity is the same, then the sum becomes easy to solve, but complications creep in when the velocity changes and initial and final velocity enters the scene.

Initial velocity: the velocity of an object when it starts the journey in a particular direction.

Final velocity: the velocity of an object when it ends the journey it started in a particular direction.

Calculation of velocity

According to the definition of velocity, it is a measurement of distance per unit of time. 

So, V = d/t where V= velocity, d= distance travelled by the object, t= time taken by the object to travel that distance.

For the calculation of final velocity: 

To find out the final velocity of an object, first, find out the force of the object and its mass as well. Divide the force by the mass and multiply the answer by the time taken by the object to accelerate.

Other aspects of velocity

The SI unit of velocity- m/s or  (m.s-1).

Other units used: mph, ft/s.

Dimension: LT-1.

What is the dimensional formula of velocity?

The dimensional formula of velocity is represented as M0 L1 T-1

M = Mass.

L = Length.

T = Time.

Derivation of the formula:

Velocity = Displacement x Time-1_____ (1)

Dimensional formula of Displacement and time is [M0 L1 T0] and [M0 L0 T1] respectively_____(2)

By substituting (2) in (1) we will get,

Velocity = Displacement x Time-1

or, V = [M0 L1 T -1]

Therefore, velocity is dimensionally written as [M0 L1 T -1].

Average velocity

Average velocity is the displacement of the object divided by the time intervals where the displacement occurred. The value of the average velocity can be either negative or positive, depending on the sign of the displacement.

Average velocity = Δ position/time = displacement/time.

Example

A person drops the ball from an extremely tall building. What will be the ball’s velocity after 2.60 seconds?

In solving this sum, you need to first find out the height of the building or the distance the egg travels and also the final velocity.

The height of the building can be represented as, d = vI × t + 0.5 × a × t2 (d= distance, v1=initial velocity, t= time and a= acceleration).

The final velocity can be represented as, vf = vi + a×t (vf = final velocity, vi = initial velocity, a = acceleration and t = time). 

In this sum, since the egg was dropped and not thrown, the initial velocity will be zero. 

Next, all that is needed to be done is to incorporate the proper values in the equation and find the answer. Here the velocity will be represented with a minus sign as it was dropped. If it was thrown in the air, it would have a positive sign.

Conclusion

To understand and work with the sums of kinetics, studying velocity and all the aspects associated with it is extremely important. With proper concentration and a clear concept of the topic, one can easily solve any sum. With velocity problems, it is important to know which equation to use and then put the correct values to get the right answer.