Equation of Motion:

Relation among velocity, distance, time and acceleration is called equations of motion. There are three equations of motion:

First Equation of Motion:

The final velocity (v) of a moving object with uniform acceleration (a) after time, t.

Let, the initial velocity = u.
Final velocity = v.
Time = t
Acceleration = a

We know that, Acceleration (a) `=(text{Change in velocity})/(text{Time taken})`

`=> a=(text{Final velocity-Initial velocity})/text{Time taken}`





`=>v=u+at` ---(i)

This equation is known as first equation of motion.

Second Equation of Motion:

Distance covered in time (t) by a moving body.

Let, Initial velocity of the object = u
Final velocity of the object = v
Acceleration = a
Time = t
Distance covered in given time = s

We know that,

Average velocity `=(text{Initial velocity+Final velocity})/2`

∴ Average velocity `=(u+v)/2` ----(ii)

We know that, Distance covered (s) in given time = Average velocity x Time

Or, s = Average velocity x Time -----------------(iii)

After substituting the value of average velocity from equation (ii) we get


After substituting the value of ā€˜vā€™ from first equation of motion we get,


`=>s=(u+u+at)/2 xxt`

`=>s=(2u+at)/2 xxt`

`=> s=(2ut+at^2)/2`


`=>s= ut+(at^2)/2`

`=>s=ut+1/2 at^2` ----(iv)

The above equation is known as Second equation of motion.

Third Equation of Motion:

The third equation of motion is derived by substituting the value of time (t) from first equation of motion.

We know from first equation of motion, `v=u+at`



`=>t=(v-u)/a` -----(v)

We know that the second equation of motion is, `s=ut+1/2at^2`

By substituting the value of `t` from euqation (v) we get



`=>s=(u(v-u))/a +(axx(v-u)^2)/(2xxaxxa)`

`=>s=(uv-u^2)/a + ((v-u)^2)/(2a)`






`=>v^2=u^2+2as` ---(vi)

This is called the Third equation of motion.

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