Initial Velocity Formula

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Different Forms of Initial Velocity Formula

Three Different Formula of Initial Velocity Derived from Equations of Motion

Motion is an important part of the concepts you learn in physics. It describes how a body moves from one location to the other at a particular time period. This is where you will also learn the three laws of motion. A new term will emerge with the name initial velocity. In this section, we will discuss and learn the meaning and use of the initial velocity formula in different aspects. We will also study how this formula is being derived and used to solve problems.

Initial Velocity: What is it and How Its Formula is Derived?

In the advanced classes of physics, we learn how to determine the value of a body’s motion. This becomes difficult when the body is not in uniform motion. The motion changes with time. It either increases or decreases. This is when the concept of initial velocity comes into the discussion. It is where we will derive and use the initial vertical velocity formula.

Let us suppose the initial velocity is denoted by ‘u’, the final velocity is denoted by ‘v’, the time taken to increase the velocity from ‘u’ to ‘v’ is‘t’, then the acceleration ‘a’ is:

a = (v-u)/t

If we rearrange it, we will find the formula for the first equation of motion. It is:

v = u + at

Now, if we rearrange it again, we will find the formula of the initial velocity equation to determine its value.

u = v – at

If we do the same rearrangement to all the equations of motion, we will find three such unique initial horizontal velocity formula to identify the value of the initial velocity. Let us take a quick look at those formulas.

The first formula to find initial velocity is u = v – at.

The Second Formula is:

u = s/t – ½ at where ‘s’ = displacement travelled within the time period ‘t’

The third initial velocity formula physics is derived from the 3rd equation. It is:

u2 = v2 – 2as

Why Should We Learn Three Different Initial Velocity Formula?

The prime reason for learning three different formulas for identifying the initial velocity is convenience. You can see that all the formulas have something unique. The first formula can derive the value of initial velocity without ‘s’ or displacement used. The second formula can derive the value of ‘u’ without ‘v’. Similarly, the third formula can derive the value of ‘u’ without using ‘t’.


Learning three different formulas with the initial velocity equation will help you identify the value of initial velocity easily. You will also understand the equations of motion better and use them to calculate the values of any term using the data given in a problem.

FAQ (Frequently Asked Questions)

1. How can you derive the initial vertical velocity formula?

When a body is under acceleration or retardation, all the equations of motion will be valid to use. This is why it becomes easier to derive the formula of vertical motion. All you have to check is whether the body is accelerating or retarding and then adjust the formula.

2. Why should you learn how to determine the initial velocity?

When you study and understand the three equations of motion, you will find it easier to understand the three laws of motion too. You will be able to apply the initial horizontal velocity formula to explain your answers well.

3. How can you understand the initial velocity formula?

It is easier to understand the formula when you derive it on your own. Understand the meaning of all terms and rearrange them to find the initial velocity formula.