Question

Derived the expression for distance covered in nth

Answer 1

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)