Question

How can we derive the distance travelled in nth second by calculus method? Please derive it...

Answer 1

1. displacement in nth second
2. distance covered in nth second

Answer 2

answer: if sn is the distance covered by a body in n- Seconds and sn_1 is the distance covered by the body in n_1 seconds then,

S nth = Sn_Sn_1

since we have

s = ut + 1/2 at^2

if t=n then,

Sn =un +1/2 an^2

1. if t=n-1 then,

Sn-1 = u(n-1) +1/2a( n-1) ^2

subtracting 2 from 1 we get

Snth= un +1/2an ^2 _ ( u(n-1) +1/2 a (n_1)^2 )