Derive the equation for uniform accelerated motion for the displacemen

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

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

Answer»

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,

∵ $S_{nth} = S_{n} - S_{n - 1}$