Question

derive mathematically second equation of motion ​

Answer 1

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(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.

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Answer 2

ꜱᴇᴄᴏɴᴅ ᴇQᴜᴀᴛɪᴏɴ ᴏꜰ ᴍᴏᴛɪᴏɴ=s=ut+1/2 at^2

=>This equation will be solves by the formula of area of rectangle and triangle.

=>OA×OC+1/2(AD×BD)

=>Substituting OA=u(intial velocity) and AD=t(time) And BD=at.

=>s=u×t+1/2(t×at)

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Hope this helps u dear mate ✌✌