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 '. If the initial velocity is ( ^{prime} 2 u^{prime}, ) with the same force 'F', the distance travelled before it comes to rest is 's ( _{2}^{prime} . ) Then

# 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 '. If the initial velocity is ( ^{prime} 2 u^{prime}, ) with the same force 'F', the distance travelled before it comes to rest is 's ( _{2}^{prime} . ) Then

(A) ( mathrm{s}_{2}=2 mathrm{s}_{1} )

(B) ( s_{2}=frac{s_{1}}{2} )

( (mathrm{C}) mathrm{s}_{2}=mathrm{s}_{1} )

( (mathrm{D}) mathrm{s}_{2}=4 mathrm{s}_{1} )

Solution

[

cos t rightarrow u=u quad a c c u=a

]

[

begin{array}{l}

Rightarrow quad 0=u^{2}-2 a S_{1}

quad=>quad S_{1}=frac{u^{2}}{2 a}

end{array}

]

If force is pame ( Rightarrow ) accen ( =a ) ( operatorname{vew} U=24 )

( Rightarrow 0=4 u^{2}-2 a s_{2} )

[

Rightarrow quad S_{2}=4 cdot frac{u^{2}}{2 a}=4 S_{1}

]