3 equation of motion

THREE EQUATION’S OF

MOTION
NAME :- ASHWANI KUMAR
SUBJECT:-PHYSICS PROJECT(EQUATION OF
MOTION)

•First Equation of Motion
The first equation of motion is v=u + at. It gives the
velocity acquired by a body in time t.
Consider a body having initial velocity ‘u’. Suppose it is
subjected to a uniform acceleration ‘a’ so that after
time ‘t’ its final velocity becomes ‘v’. Now, from the
definition of acceleration we know that;
—> Acceleration=Change in velocity
Time taken
—> Acceleration=Final velocity –Initial velocity
Time taken
—> a=v - u
t
—> at=v - u
—> v=u + at

•Second Equation of Motion
The second equation of motion is s=ut + 1at. It gives
2
the distance traveled by a body in time t.
Consider a body having initial velocity ‘u’ and a uniform
acceleration ‘a’ for time ‘t’ so that its final velocity
becomes ‘v’. .Let the distance traveled by the body in
this time ‘s’. The distance travelled by a moving body
in time ‘t’ can be found out by considering its average
velocity. Since the initial velocity of the body is ‘u’ and
its final; velocity is ‘v’ ,the average velocity is given by:
—> Average velocity=Initial velocity+ final velocity
2
—> Average velocity=u + v
2

Distance travelled= average velocity x Time

—> S=(u + v) x t …………………….(1)
2
From the first equation of motion we have ,v=u + at.
Putting the value of v in equation (1), we get
—> S=(u+ u+ at) x t
2
—> S=(2u+at) x t
2
—> S=2ut+ at2
2

—> S= ut+1at2
2

•Third Equation of Motion
The third equation of motion is v=u+2as. It gives
the velocity acquired by a body in
traveling a distance ‘s’
Consider a body having initial velocity ‘u’ and a uniform
acceleration ‘a’ for time ‘t’ so that its final velocity
becomes ‘v’. .Let the distance traveled by the body in
this time ‘s’. The distance travelled by a moving body
in time ‘t’ can be found out by considering its average
velocity. Since the initial velocity of the body is ‘u’ and
its final; velocity is ‘v’ ,the average velocity is given by:
The third equation of motion can be obtained by
eliminating t between the first two equation of motion.
From second equation of motion we have;
S=ut+1at
2 ……………..(1)

And from the first equation of motion we have;

—> v=u + at
This can be rearranged and written as
—> at=v - u
—> t=v - u
a
Putting the value of tin equation (1)we get;
—> S=u (v-a)+1a(v-u/a)
2
—> S=uv-u+a(v+u-2uv)
a 2a
—> S=2uv-2u+v+u-2uv
2a
—> 2as= v – u

—> V=u+2as

3 equation of motion

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3 equation of motion