Question

Write three equation of motion and derived

Answer 1

Here are the derivations of Newton's equations of motion

You're welcome!

Answer 2

The three equations of motion are:

1.v=u+at

Derivation: acceleration = v-u/t

at=v-u (solving equation where acceleration is a)

v=u+at (linear equation)

2.S=ut+1/2at^2

Derivation: distance=avg.velocity *time

=(initial velocity +final velocity /2)*time

S=u+v/2*t

From equation 1. v=u+at. Hence substituting value of v

S=u(u+at)/2*t

S=ut+1/2at^2

3.v^2=u^2+2aS

Derivation : distance travelled =avg. Velocity *time

S=u+v/2*t

By substitution of v by u+at (using derivation of second law)

t=v-u/a

Therefore,S=u+v/2*v-u/a

S =v^2-u^2/2a

v^2-u^2=2aS

v^2=u^2+2aS

Hope I was able to answer your doubt.