Question

If a body starts from rest and travels $120$ cm in the $6^{th}$ second then what is the acceleration ?

• A. $0.20m/s^2$
• B. $0.027m/s^2$
• C. $0.218m/s^2$
• D. $0.003m/s^2$

Answer 1

Answer: (C)

$0.218m/s^2$

$S=ut+0.5a{t}^2$

displacement in n-1 sec is given by:

$S_{n-1}=u(n-1)+0.5a(n-1{)}^2$

$S_{n-1}=un-u+0.5a{n}^2+0.5a(1-2n)$

displacement in n seconds is given by:

$S_n=un+0.5a{n}^2$

Subtract above equations to get the displacement in "nth" second:

$S=u+0.5a(2n-1)$

Therefore, displacement in n = 6s

$1.2=0+0.5a(12-1)$

$a=\frac{1.2}{5.5}=0.218m/s^2$