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`        how to derivea relation for the distance travelled in nth second by a uniformly accelerated body`
7 years ago

asd wer
31 Points
```										distance travelled in n seconds:
S1= un + 1/2a(n^2)
distance travelled in (n-1) seconds:
S2 = u(n-1) + 1/2a((n-1)^2)
distance travelled in nth second:
S1-S2
= u + 1/2a(2n-1)
```
7 years ago
vijay kumar pandey
32 Points
```										actually the other given answer is also correct.
displacement in the nth second,we r talking about.suppose accleration is a and the initial velocity is u.
s=ut+1/2at^2.
if i will be said to find out the displacement in the nth second.so i will find out the displacement in the n-1 th second,can be easily found by the above given equation.
s(n-1)=u(n-1)+1/2a(n-1)^2=un-u+1/2a(n^2-2n+1)=un-u+1/2an^2-an+1/2a
now this is the total displacement in n-1 second.in n second the displacent is :
s(n)=un+1/2an^2
so i f i want the displacement in that n second nly,so i need to subtract the total displacement in n second and in n-1 second.
s(n)-s(n-1)=un+1/2an^2-un+u-1/2an^2+an-1/2a=u+an-1/2a=u+1/2a(2n-1).
actually to make this answer correct u need to write the seconds (dimensionally correct)
so,u(1s)+1/2a(2n-1s)(1s) is the correct answer.if u will keep on writing the units from the first then u will get this equation only.
```
7 years ago
Nikita
11 Points
```										Distance travelled by a uniformly accelerated body in nth second can be obtained by subtracting the distance travelled by the body in (n-1) second from the distance travelled by the body in n seconds.If, u= initial velocity of the body;a= uniform acceleration of the body;Sn,Sn-1= distances travelled by the body in n seconds and (n-1) seconds respectively,Dn = distance travelled in nth second.Then,     Dn = Sn-Sn-1We know that the distance travelled in t seconds is given by; S= ut+1/2 at×t=> distance travelled in n seconds is,                 Sn= un+1/2an×nDistance travelled in (n-1) seconds is,          Sn-1= u (n-1)+1/2a (n-1)(n-1)Now putting these values in, Dn=Sn-Sn-1We get, Dn=[un+1/2an×n]-[u (n-1)+1/2a (n-1)(n-1)]     =un+1/2an×n-un+u-1/2an×n+an-a/2     =u+an-a/2     =u+a (n-1/2)      or  Dn= u+a/2 (2n-1)
```
5 months ago
Amar kumal
19 Points
```										Home » Forum » Modern Physics » kinematicshow to derivea relation for the distance travelled in nth second by a uniformly accelerated body7 years agoAnswers : (3)distance travelled in n seconds:S1= un + 1/2a(n^2)distance travelled in (n-1) seconds:S2 = u(n-1) + 1/2a((n-1)^2)distance travelled in nth second:S1-S2= u + 1/2a(2n-1)
```
4 months ago
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