Initial Velocity

Let us start with the difference between velocity and speed. It is quite obvious after all the discussion about vector and non vector quantities. Speed is basically a measurement with no direction. In case of velocity we also consider direction.

Velocity can be of two types: initial velocity and final velocity. When the object starts its motion then we can say that the initial velocity is zero as it has just started from rest. Similarly we can also consider int. velocity as some constant value. Let us take an example of a car starting from rest and attaining a velocity of 50 km per hour in 1 hour time period.

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So here we can say that the int. velocity of the car is zero and the final velocity is 50 km per hour, directed northwards. Here mentioning the direction is very important as velocity is all about direction, it being a vector quantity.

Let us now discuss Initial velocity formula. We have 3 equations of motion that have a reference to int. velocity and hence can be used for its calculation.
They are as follows:
V = u + a t ------------ > (1)
Here v is the final velocity
U is the int. velocity
A is the acceleration
T is the time period.
So u = v – a t
Also the second equation is
S = u t + 1.5 a t^2 - - - - - - >(2)
Here s is the distance covered in time interval t.
A is the acceleration
We also have a third equation for calculating velocity. It is as follows:
V^2 = u^2 + 2 a s - - - - - - -> (3)

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Here v is the final velocity and a is the initial velocity.
All these are initial velocity equation. We can also say that u^2 = v^2 – 2 a s - - - - - - - > (4)
Let us take a real world example to clear the concept. Let us assume the final velocity of the car is 50 m per sec and the time taken to complete the journey is 2 hours. Also the acceleration is 10 meter per second square. So now using first formula we will try to calculate the initial velocity.
Hence v = u + a t
Or 50 = u + 20
U = 50 – 20 = 30 m per sec