Question

Derive mathematical the first equation of motion v = u + at

Answer 1

Explanation:

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Answer 2

To derive :

Mathematical formulation of 1st equation of Kinematics i.e v = u + at , where v is the final velocity , u is the initial velocity , a is the acceleration and t is the time taken.

Proof:

We shall prove this equation in an algebraic method .

Acceleration is defined as the instantaneous rate of change of velocity with respect to time.

Mathematically , it can be represented as:

$\therefore \: \: a = \dfrac{\Delta (velocity)}{time}$

$= > a = \dfrac{v - u}{t}$

$= > v - u = at$

$= > v = u + at$

[Hence Proved]

It can also be proved in Graphical Manner:

Let's take a acceleration vs time graph , the area of that graph shall give us the change in velocity ,

Change in velocity = Area of graph

=> v - u = Area of rectangle

=> v - u = a × t

=> v = u + at