Question

Derive all three Equations of motion.

Answer 1

wait let me explain u by a photo which derive equation of motion by using graph
I hope u understand by this photo

Answer 2

v=u +at ,it us is a 1st equation of motion.

a=v-u
t.

at=v-u
at+u=v
v=u+at

2nd equation of motion

s=ut/+1/2×at²
distance={u+v/2}×t {distance=average velocity ×time} average velocity =speed because motion is uniform

s={(u+v/2)*t}
s={(u+u+at/2)*t} {v=u+at ,above equation}
s=(2u/2+at/2) t. (in 2u ,2 is cancelled by 2)
s=(u+1/at)*t
s=ut+1/2at²

3rd equation of the motion

v²=u²+2as


v=u+at
(v)²=(u+at)² (squaring on both side)
v²=u²+a²t²+2*u**at (u+at) breaks on the formula of (a+b)²
v²=u²+2a(ut+1/2at²)
v²=u²+2as .( s=ut+ 1/2at²)

in all this equation
a=acceleration
v=velocity
u=initial velocity
t=time
s=distance