Question

Two cars started moving with initial velocities v and 2v. For the same
deceleration, their respective stopping distances are in the ratio
(A) 1:1 (B) 1:2 (C) 1:4
(D) 2:1
(E) 4:1
​

Answer 1

Answer:

C

Explanation:

using V^2 = U^2 - 2*a*s

s = v^2 / (2*a)

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{s_{1}: {s_{2}} =1 : 4}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline{\bold{Given :}}} \\ \tt: \implies Initial \: velocities \: of \: two \: car = v \: and \: 2v \\ \\ \tt: \implies Deceleration \: of \: car \: a = Deceleration \: of \: car \:b \\ \\ \red{\underline{\bold{To \: Find :}}} \\ \tt: \implies Ratio \: of \: their \: stopping \: distance = ?$

• According to given question :

$\green{\star } \tt \: Final \: velocity \: of \: car \: a =Final \: velocity \: of \: car \: b \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies {v}^{2} = {u}^{2} + 2as_{1} \\ \\ \tt: \implies {0}^{2} = {v}^{2} + 2as_{1}\\ \\ \tt: \implies { - v}^{2} = 2as_{1} \\ \\ \tt: \implies s_{1} = \frac{ - {v}^{2} }{2a} - - - - - (1) \\ \\ \bold{Similarly : } \\ \tt: \implies {v}^{2} = {u}^{2} + 2a s_{2} \\ \\ \tt: \implies {0}^{2} = {(2v)}^{2} + 2a s_{2} \\ \\ \tt: \implies s_{2} = \frac{ - 4 {v}^{2} }{2a} \\ \\ \tt: \implies s_{2} = \frac{ - 2 {v}^{2} }{a} - - - - - (2) \\ \\ \text{Dividing \: (1) \: by \: (2)} \\ \\ \tt: \implies \frac{ s_{1}}{s_{2}} = \huge{\frac{ \frac{ - {v}^{2} }{2a} }{ \frac{ - 2{v}^{2} }{a} } } \\ \\ \tt: \implies \frac{ s_{1}}{s_{2}} = \frac{1}{4} \\ \\ \green{\tt: \implies { s_{1}} : {s_{2}} =1 : 4}$