11. A body starts from rest, what is the ratio of the distance travelled by the body during the 4th and 3rd seconds?

11. A body starts from rest, what is the ratio of the distance travelled by the body during the 4th and 3rd seconds?

(a) \( \frac{7}{5} \)

(b) \( \frac{5}{7} \)

(c) \( \frac{7}{3} \)

(d) \( \frac{3}{7} \)

Answer :  (a) \( \frac{7}{5} \)

\( s = ut + \frac{1}{2}at^2 \)

\(u=0 \Rightarrow s = \frac{1}{2}at^2 \)

\( s_{\text{4th second}} = s_4 - s_3 \)

\( = \frac{1}{2}a(4^2) - \frac{1}{2}a(3^2) \)

\( = \frac{1}{2}a(16 - 9) \)

\( = \frac{7a}{2} \)

\( s_{\text{3rd second}} = s_3 - s_2 \)

\( = \frac{1}{2}a(3^2) - \frac{1}{2}a(2^2) \)

\( = \frac{1}{2}a(9 - 4) \)

\( = \frac{5a}{2} \)

\( \frac{s_{\text{4th second}}}{s_{\text{3rd second}}} = \frac{\frac{7a}{2}}{\frac{5a}{2}} \)

\( = \frac{7}{5} \)