Question

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Prove s=ut +1/2at^2??​

Answer 1

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

Answer:

$hello$

There are TWO kinematics equations.

Acceleration = velocity change / time or a=(v-u)/t

normally rearranged to v=u+at

and displacement = average velocity multiplied by time

usually rearranged to s = t(u+v)/2

Putting v of the first into the second gives s = ut + 1/2 at^2

Two other substitutions lead to the other suvat equations:

v ^2 = u^2 + 2as

And s = vt - 1/2 at^2