Speeds of two identical cars are u and 4 u at a specific instant. The ratio of the respective distances at which the two cars are stopped from that instant is :

Question

Speeds of two identical cars are u and 4 u at a specific instant. The ratio of the respective distances at which the two cars are stopped from that instant is : (A) 1: 1 (B) 1: 4 (C) 1: 8 (D) 1: 16

Tardigrade Admin · Accepted Answer

In this question the cars are identical means coefficient of friction between the tyre and the ground is. same for both the cars, as a result retardation is same for both the cars equal to

μ

g. Let first car travel distance

s_{1}

, before stopping while second car travel distance

s_{2}

, then from

v^{2} = u^{2} - 2 a s

\Rightarrow 0 = u^{2} - 2 μg \times s_{1}

\Rightarrow s_{1} = \frac{u ^{2}}{2 μg}

and

0 = (4 u)^{2} - 2 μg \times s_{2}

\Rightarrow s_{2} = \frac{16 u ^{2}}{2 μg} = 16 s_{1}

\Rightarrow \frac{s _{1}}{s _{2}} = \frac{1}{16}

Q. Speeds of two identical cars are u and 4u at a specific instant. The ratio of the respective distances at which the two cars are stopped from that instant is :

1: 1

1: 4

1: 8

1: 16

Q. Speeds of two identical cars are $u$ and $4 u$ at a specific instant. The ratio of the respective distances at which the two cars are stopped from that instant is :