Question

derive the relation .v2=U2+2as​

Answer 1

Answer:

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Explanation:

For getting the third law of motion equation, we use both of the equations of motion

S = ut + 1/2at2__________(1)

v = u + at _____________ (2)

t = (v – u)/a

Substitute the value of t in equation (1)

S = ut + 1/2at2

\(S = u\frac{(v-u)}{a}+\frac{1}{2}a(\frac{v-u}{a})^{2}\)

2aS = 2u(v−u) + (v−u)2

2aS = 2uv − 2u2 + v2 − 2uv + u2

2aS = v2 − u2

v2 = u2 + 2aS

Answer 2

Explanation:

Derivation of v²=u²+2aS

Distance Travelled=Average Velocity×Time

Now,

Average Velocity=(Initial Velocity+Final Velocity)/2

u+v

= --------

2

Now putting Average velocity in Distance Formula

Distance(S)= (u+v)/2×t --------------( 1 )

Now As we know,

v=u+at

v - u

t = -----------------

a

Substitute the value of t in distance Formula ( 1 )

u+v. v - u

S = ---------- × --------------

2. a

v²-u²

S= ------------------

2a

v² - u²= 2as

v²=u²+2aS

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