Question

using calculus, to show v^2 =u^2 +2as​

Answer 1

To Show :

• v² = u + 2as

Required Solution :

When a body is moving with uniform acceleration, the distance travelled by the body is given by :$\:$

Distance = Average velocity × time .....❶

If u and v are the initial and final velocity then we can write

⇛ s = { v + u /2} × t .....❷

By the first equation of motion

⇛ v = u + at

This gives ,

⇛ t = { V - U/a}

Substituting the value of t in the equation .....❷) we get,

⇛ s = ( v + u/2) × (V - U/a)

This gives ,

⇛ 2as = v² - u²

Therefore ,

⇛ v² = 2as + u²

⇛ v² = u² + 2as

Hence Solved !!