Question

A particle starts from rest and moves under constant acceleration in a straight line. If time taken by it to cover displacement d is 10 s then time taken by it to cover next d displacement is

• A. 3.2 s
• B. 4.1 s
• C. 2. 6 s
• D. 1. 4 s

Answer 1

The correct option is B 4.1 s

Initial velocity = 0
$s=ut+\frac{1}{2}a{t}^2,u=0$
$s=\frac{1}{2}a{t}^2,d=\frac{1}{2}a\times 100$
$a=\frac{d}{50}$
$v=u+At$
$v=\frac{d}{50}\times 10=\frac{d}{5}$.
Covering next d displacement
$u=\frac{d}{5}a=\frac{d}{50}t=?$
s = d
$s=ut+\frac{1}{2}a{t}^{2}d=\frac{d}{5}t+\frac{1}{2}\times \frac{d}{50}{t}^{2}1=\frac{t}{5}+\frac{t^2}{100}{t}^2+20t-100=0t^2+20t=100t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-20\pm \sqrt{800}}{2}=-10+10\sqrt{2}=4.1seconds$