Why do we have to use the s=ut+1/2 at^2 formula?
The mathematically proven equations are as follows
(1) First equation of Motion:
V = u + at
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
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.
Hope u got it.