Question

solve the all equation of motion, clearly.......

Answer 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.

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.

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
This is the third equation of motion