The equations of motion describe the physical relationships between displacement, velocity, acceleration, and time. There are three equations of motion that are commonly used to solve problems involving motion in a straight line. These equations can be derived from the definitions of displacement, velocity, and acceleration.


This equation relates the final velocity of an object (v) to its initial velocity (u), acceleration (a), and time (t). The derivation of this equation is as follows:

- The definition of acceleration is a = (v - u)/t
- Rearranging the equation gives v = u + at


This equation relates the displacement (s) of an object to its initial velocity (u), acceleration (a), and time (t). The derivation of this equation is as follows:

- The definition of average velocity is v = s/t
- Rearranging the equation gives s = vt
- Using equation 1, we can substitute v = u + at into the equation to get s = (u + at)t
- Simplifying gives s = ut + 1/2at^2


This equation relates the final velocity (v) and initial velocity (u) of an object to its acceleration (a) and displacement (s). The derivation of this equation is as follows:

- Using equation 1, we can substitute v = u + at into the equation to get v^2 = u^2 + 2as
- Rearranging the equation gives v^2 - u^2 = 2as


The three equations of motion can be derived from the definitions of displacement, velocity, and acceleration. These equations are useful for solving problems involving motion in a straight line.

(1) 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