Question

Prove second equation of motion.
Class 9th

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.

Answer 2

Prove second equation of motion.

Good question,

Here is your perfect answer!

To proof S = ut + at²/2

Here S refers to displacement,

u initial velocity,

a for acceleration,

t for time.

We know S = (u+v)/2 * t

We know v = u + at,

=) S = (u + u +at)/2 * t

=) S = (2u + at) /2* t

=) S = 2ut /2 + at²/2

=) S = ut + at²/2.