S=ut+1/2att. By the graph and mathematical …

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 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. Hope u got it.