Question

Derive the equation for uniform accelerated motion for the displacement covered in its nth second of its motion. (Sn=u+a(n-½ ))

Answer 1

To Prove ⇒ $S_{nth} = un + \frac{1}{2} a (2n - 1)$

Proof ⇒

Let us consider that the object is moving with the initial velocity u and have the uniform acceleration of a. Then the displacement in the nth second will be given by,

∵ $S_{nth} = S_{n} - S_{n - 1}$

∴ $S_{nth} = un + \frac{1}{2} an^2 - u(n - 1) - \frac{1}{2} a (n - 1)^2$

⇒ $S_{nth} = u(n - n + 1) + \frac{1}{2}a(n^2 - n^2 - 1 - 2n)$

⇒ $S_{nth} = u + \frac{1}{2}a(2n - 1)$

Hence Proved.

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