Question

derive V=u+at with examples

Answer 1

Explanation:

Derivation of v = u + at

The first equation of motion

First, let us know the definition of Acceleration:-

Acceleration :-

The rate of change in velocity is called acceleration.

• Final velocity = v

• Initial velocity = u

• Acceleration = a

• Time = t

Change in velocity = Final velocity - Initial velocity = v - u

$\rm \implies Acceleration \: = \dfrac{v - u}{t}$

$\rm \implies a \: = \dfrac{v - u}{t}$

$\rm \implies at \: = {v - u}$

$\rm \implies at + u \: = {v }$

$\rm \implies v = u + at$

There is an alternative method for the derivation of v = u + at

By using integration method:-

Acceleration = a

$\rm \implies a = \dfrac{dv}{dt}$

$\rm \implies dv = a \times dt$

Velocity changes from u to v from time t = 0 to t = t

By applying integration on both sides.

$\rm \implies \int_{u} ^{v}dv = \int_{0}^{t} a \times dt$

$\rm \implies v - u = a(t - 0)$

$\rm \implies v - u = at$

$\rm \implies v =u+ at$

Hence Proved