Question

derive the second equation of motion by mathematical method​

Answer 1

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Here is your answer......

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Let the distance travelled by the object be “s”.

We know that,

→Distance = Average velocity × time

→Average velocity = (u+v)/2

Then s=(u+v)/2×t

According to first equation if motion,

v = u + at

substituting the value of v in above equation

s = (u+u+at)/2 x t

→s = (2u+at)/2 × t

→s = (2ut+at²)/2

→s = 2ut/2 + at²/2

→s=ut+1/2at²

Hence derived.

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Answer 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