Question

write second equation of motion

Answer 1

s=ut+1/2at^2 this is the second equation if motion

Answer 2

FIRST EQUATION OF MOTION
Vf = Vi + at

Consider a body initial moving with velocity "Vi". After certain interval of time "t", its velocity becomes "Vf". Now
Change in velocity = Vf - Vi
OR
DV =Vf – Vi
Due to change in velocity, an acceleration "a" is produced in the body. Acceleration is given by
a = DV/t
Putting the value of "DV"
a = (Vf – Vi)/t
at = Vf – Vi
at + Vi =Vf
OR

SECOND EQUATION OF MOTION
OR
S = Vit + 1/2at2

Consider a car moving on a straight road with an initial velocity equal to ‘Vi’. After an interval of time ‘t’ its velocity becomes ‘Vf’. Now first we will determine the average velocity of body.
Average velocity = (Initial velocity + final velocity)/2
OR
Vav = (Vi + Vf)/2
but Vf = Vi + at
Putting the value of Vf
Vav = (Vi + Vi + at)/2
Vav = (2Vi + at)/2
Vav = 2Vi/2 + at/2
Vav = Vi + at/2
Vav = Vi + 1/2at.......................................(i)
we know that
S = Vav x t
Putting the value of ‘Vav’
S = [Vi + 1/2at] t

THIRD EQUATION OF MOTION
OR
2aS = Vf2 – Vi2

Initial velocity, final velocity, acceleration, and distance are related in third equation of motion.
Consider a body moving initially with velocity ‘Vi’. After certain interval of time its velocity becomes ‘Vf’. Due to change in velocity, acceleration ‘a’ is produced in the body. Let the body travels a distance of ‘s’ meters.
According to first equation of motion:
Vf = Vi + at
OR
Vf – Vi = at
OR
(Vf – Vi)/a = t....................(i)
Average velocity of body is given by:
Vav = (Initial velocity + Final velocity)/2
Vav = (Vi + Vf)/2.................. (ii)
we know that :
S = Vav x t.................. (ii)
Putting the value of Vav and t from equation (i) and (ii) in equation (iii)

S = { (Vf + Vi)/2} { (Vf – Vi)/a}
2aS = (Vf + Vi)(Vf – Vi)
According to [ (a+b)(a-b)=a2-b2]