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

Answer 1

Answer: (D)

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 $\mu$ g. Let first car travel distance $s_{1}$, before stopping while second car travel distance $s_{2}$, then from
$v^{2}=u^{2}-2 a s$
$\Rightarrow \quad 0=u^{2}-2 \mu g \times s_{1}$
$\Rightarrow s_{1}=\frac{u^{2}}{2 \mu g}$
and $0=(4 u)^{2}-2 \mu g \times s_{2}$
$\Rightarrow s_{2}=\frac{16 u^{2}}{2 \mu g}=16 s_{1}$
$\Rightarrow \frac{s_{1}}{s_{2}}=\frac{1}{16}$