Question

Derive the relation S=ut + 1/2 at²​

Answer 1

Hey There,

To derive : s = it + 1/2 at^2

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Answer 2

Explanation:

The second equation of motion is s = ut+½at².

Suppose a body has an initial velocity 'u'and a uniform acceleration 'a' for time 't' so that its final velocity becomes 'v'. Let the distance travelled by the body in this time 's'. The distance travelled by a moving body in time 't' can be found out by considering its average velocity. Since the initial velocity of the body is 'u' and its fimal velocity is 'v', the average velocity is given by :

Average velocity = Initial velocitiy+ Final velocity / 2

That is , Average velocity = u+v / 2

Also, Distance travelled = Average velocity × Time

So, s = (u+v) /2×t .....(1)

From the first equation of motion we have, v = u+at .Putting this value of v in equation (1) , we get :

s = (u+u+at) × t / 2

s = (2u+ at) ×t /2

s = 2ut + at² / 2

or s = ut + ½at²

I hope it helps you.

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