Question

A body of mass '$m$' is travelling with a velocity '$u$'. When a constant retarding force '$F$' is applied, it comes to rest after travelling a distance '$s_1$'. If the initial velocity is '$2u$', with the same force '$F$', the distance travelled before it comes to rest is '$s_2$'. Then

• A. $s_2=2s_1$
• B. $s_2=\frac{s_1}{2}$
• C. $s_2=s_1$
• D. $s_2=4s_1$

Answer 1

The correct option is D $s_2=4s_1$

According to Newton's second law of motion,

$a=-F/m$ ($-ve$ sign as the force is retarding)

According to third equation of motion,

$v^2=u^2+2as$

Given for $v=0,u=u$,

Displacement is $s_1$

$⟹s_1=\frac{u^2}{2a}=\frac{u^{2}m}{2F}................\left(i\right)$

Given for second scenario,

$v=0,u=2u$,

Displacement is $s_2$

$⟹s_2=\frac{(2u{)}^2}{2a}=\frac{2u^{2}m}{F}................\left(ii\right)$

From (i) and (ii),

$s_2=4s_1$