question_answer

The speeds of two identical cars are u and 4u at a specific instant. What is the ratio of the respective distances in which the two cars are stopped from that instant?

Answer:

Car-1	Car-2
\[{{u}_{1}}=u\]	\[{{u}_{2}}=4u\]
\[{{v}_{1}}=0\]	\[{{v}_{2}}=0\]
\[{{S}_{1}}:{{S}_{2}}=?\]

We know that, \[{{v}^{2}}-{{u}^{2}}\propto S\] \[\Rightarrow \frac{{{S}_{1}}}{{{S}_{2}}}=\frac{V_{1}^{2}-u_{1}^{2}}{V_{2}^{2}-u_{1}^{2}}=\frac{{{0}^{2}}-{{u}^{2}}}{{{0}^{2}}-{{(4u)}^{2}}}\Rightarrow \frac{{{S}_{1}}}{{{S}_{2}}}=\frac{1}{16}\]