Question

derivation of all three equation of motion

Answer 1

_____ hey mate______


here is your answer

First equation of Motion:

V = u + at
soln.
Consider a body of mass “m” having initial velocity “u”.Let after time “t” its final velocity becomes “v” due to uniform acceleration “a”.

Now we know that:
Acceleration = change in velocity/Time taken

=> Acceleration = Final velocity-Initial velocity / time taken

=> a = v-u /t
=>at = v-u

or v = u + at
This is the first equation of motion.
—————————————-
(2) Second equation of motion:
s = ut + 1/2 at^2

sol.
Let the distance travelled by the body be “s”.
We know that
Distance = Average velocity X Time

Also, Average velocity = (u+v)/2

.: Distance (t) = (u+v)/2 X t …….eq.(1)

Again we know that:
v = u + at
substituting this value of “v” in eq.(2), we get

s = (u+u+at)/2 x t
=>s = (2u+at)/2 X t
=>s = (2ut+at^2)/2
=>s = 2ut/2 + at^2/2

or s = ut +1/2 at^2

This is the 2nd equation of motion.
……………………………………………………………
(3) Third equation of Motion
v^2 = u^2 +2as

sol.
We know that
V = u + at
=> v-u = at
or t = (v-u)/a ………..eq.(3)

Also we know that
Distance = average velocity X Time
.: s = [(v+u)/2] X [(v-u)/a]
=> s = (v^2 – u^2)/2a

=>2as = v^2 – u^2

or v^2 = u^2 + 2as

This is the third equation of motion.


hope this will help u!!!!

Answer 2

$\huge \bf{HEY \: FRIENDS!!}$


------------------------------------------------------


$\huge \bf \underline{Here \: is \: your \: answer ↑}$

⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆


$\bf \boxed{See \: the \: attachment \: for \: your \: answer}$

⤴⤴⤴⤴⤴⤴⤴⤴⤴⤴⤴⤴⤴⤴


$\huge \boxed{THANKS}$


$\huge \bf \underline{Hope \: it \: is \: helpful \: for \: you}$