Question

Derive following motion equtions
a) v=u+at​

Answer 1

Mathematical Way :-

Consider a body having initial velocity u. Suppose it is subjected to a uniform acceleration a so that after time t its final velocity v. Now from the defination of acceleration we know that :

$\leadsto \sf{Acceleration = \frac{Change\:in\:velocity}{Time\:Taken} }$

$\leadsto \sf{a = \frac{Final\:velocity-Initial\:velocity}{Time\:Taken} }$

$\sf \leadsto{v = u + at}$

$\leadsto \sf{a = \frac{v - u}{t} }$

$\leadsto \sf{at = v - u}$

$\leadsto \sf{v = u + at} \: \orange\bigstar$

Graphical Way :- [ Refer to the attachment ]

$\dashrightarrow \sf{slope \: AB= \frac{BC}{AC} }$

Slope AB = Acceleration

$\dashrightarrow \sf{a = \frac{v - u}{t} }$

$\dashrightarrow\sf{v - u =at }$

$\dashrightarrow \boxed{\sf \purple{v = u + at}} \: \orange \bigstar$

__________________....

• v stands for Final velocity
• u stands for Initial velocity
• a stands for Acceleration
• t stands for Time

More Details :-

Second equation of motion :

$\star \boxed { \sf \red{ {v}^{2} = {u}^{2} + 2as}}$

Third equation of motion :

$\star \boxed{ \sf \red{s = ut + \frac{1}{2} {at}^{2} }}$