Question

A body is in motion and it is stopped by applying retarding force. Initial speed and magnitude of force applied are as given below :

Speed	Force
V	F
2V	F/2
V/2	2F

If $S_1$, $S_2$, $S_3$ are the distance travelled before coming to rest, those can be arranged in ascending order as given below

• A. $S_1$, $S_2$, $S_3$
• B. $S_3$, $S_2$, $S_1$
• C. $S_2$, $S_1$, $S_3$
• D. $S_3$, $S_1$, $S_2$

Answer 1

The correct option is D $S_3$, $S_1$, $S_2$

using $2as=v^2-u^2$

1) $2\times \frac{F}{m}\times s=v^2$

$s=\frac{-v^{2}m}{2F}$

2) $2\times \frac{F}{2m}\times 5=-4v^2$

$s=\frac{-48v^{2}m}{F}$

3) $2\times \frac{2F}{m}\times s=(\frac{v}{2}{)}^2$

$s=-\frac{v^{2}m}{16F}$

ie $s_3<s_1<s_2$
(Considering their magnitudes only)