Question

Write the expression for distance covered in nth second by a uniformly accelerated body

Answer 1

Answer:

s= u+ a/2(n+1).

Explanation:

this distance 's' is travelled in n seconds.

This can be attained by second equation of motion, ie.

s=ut+1/2at^2.

First find s for n seconds and then for n-1 seconds.

Snth= Sn-Sn-1.

Hope this helps you!!

Answer 2

Answer:

$S_{nth}$ = $u + \frac{a(n-1)}{2}$ distance covered in nth second by a uniformly accelerated body .

Explanation:

Distance covered in nth second by a uniformly accelerated body ;

Let , u be the initial velocity  and a be the  uniform acceleration  by the body .

let $S_n$ be the distance covered by  the body in n second  and

let $S_{n-1}$ be the distance covered by the body in (n-1 ) second .

As we know that , the equation of motion for a uniformly accelerated body ,distance covered is given by ;

⇒  $S = u + \frac{1}{2} at^2$

So ,  distance covered by the body in n second ,

$S_n = un + \frac{1}{2}an^2$  

And distance covered by the body in (n-1) second ,

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

Therefore , distance covered in nth second = $S_n - S_{n-1}$

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

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

⇒$S_{nth}$ = u + $\frac{an^2 -an^2 -a +2an}{2}$

⇒$S_{nth}$ = u + $\frac{a(n-1)}{2}$

Hence , the expression for distance covered in nth second by a uniformly accelerated body is $u + \frac{a(n-1)}{2}$ .

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