Question

If a body starts with a velocity $u$ in a straight line with uniform acceleration f and covers a distance s in time t seconds, and $s_t$ denotes the distance covered by it in the $t$ seconds, then $s_2,s_4,s_6$ are in

• A. AP
• B. GP
• C. The ratio $3:7:15$
• D. none of these

Answer 1

The correct option is D none of these

Using $2^{nd}$ equation of motion the distance covered in $t^{th}$ second is
$s_t=ut+\frac{1}{2}f{t}^2$
$\therefore s_2=u\left(2\right)+\frac{1}{2}f\left(2^2\right)$
$s_4=u\left(4\right)+\frac{1}{2}f\left(4^2\right)$
$s_6=u\left(6\right)+\frac{1}{2}f\left(6^2\right)$
$\because s_4-s_2\ne s_6-s_4$
$\Rightarrow s_2,s_4,s_6$ are not in A.P
Also $\frac{s_4}{s_2}\ne \frac{s_6}{s_4}\Rightarrow s_2,s_4,s_6$ are not in G.P
Also option (c) and (d) doesn't satisfy $s_2:s_4:s_6$
Hence, all the options are incorrect