Question

a particle starting from rest is moving with uniform accelaration in a straight line. the percentage increase of the displacement of the particle in the 9th second compared to that in the immediate previous second is about :-

1.) 8.3%

2.) 20.6%

3.) 13.3%

4.) 24.5%

Answer 1

$$\begin{gathered} Dis\tan cetarvelledisgivenby: \\ s=ut+\frac{1}{2}a{t}^2 \\ u=0 \\ s=\frac{1}{2}a{t}^2 \\ {s}_9=\frac{81}{2}a \\ {s}_8=dis\tan cetravelledinprevioussecond=\frac{64}{2}a \\ s=s_9-s_8=\frac{17}{2}a \\ \%increase \\ \frac{s}{s_8}\times 100=\frac{\frac{17}{2}a}{\frac{64}{2}a}\times 100=26.65 \end{gathered}$$