Question

S=ut+1/2at2
I want with this formula in solving physic

Answer 1

Answer:

Explanation:

Correct Question :-

Derive 2nd equation of motion or s = ut + 1/2 at²

Answer :-

To derive 2nd equation, at first we have to derive 1st equation,

We know that,

Acceleration, a = Change in velocity/Time taken

⇒ a = v - u/t

⇒ at = v - u

⇒ v = u + at .... (i)

Now we have to derive 2nd equation of motion or s = ut + 1/2 at²,

Let a body moving with initial velocity u, constant acceleration a, time t and final velocity v.

We know that,

Average velocity = (Initial - Final) velocity/2

⇒ V(avg) = u + v/2 ... (ii)

If s is the displacement of the body with average velocity,

Then,

⇒ V(avg) = s/t ...(iii)

From Equation (ii) and (iii), we get

⇒ u + v/2 = s/t

Putting v's value, we get

⇒ u + u + at/2 = s/t

⇒ 2u + at/2 = s/t

By cross multiplication, we get

⇒ t(2u + at) = 2 × s

⇒ s = 2ut/2 + at/2

⇒ s = ut + 1/2 at²

Hence, derived.