Question

Proove s=u+1/2at*2 mathwmatically

Answer 1

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.

Answer 2

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Average speed = v+u/2

s = Av × time

From eq (i) v = u + at

s = u+u+at × t /2

s= 2ut +at^2/2

s = 2ut/2 + at^2/2 = s = ut + 1/2at^2

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