Answer:
Let O be the junction and AO and BO be the intersecting roads such that AO = 200 m and BO = 10 m
To find the time interval \[\Delta t\]between the moments the cars pass the intersection point, we need to know time taken by the cars to reach the junction. If \[{{t}_{1}}\]and \[{{t}_{2}}\]are times taken by the two cars to reach the junction, then \[\Delta t=|{{t}_{2}}-{{t}_{1}}|\] ….. (1)
Let us find \[{{t}_{1}}\]and \[{{t}_{2}}\]
OA
\[{{S}_{1}}=200m\]
\[{{u}_{1}}=10m/s\]
\[{{t}_{1}}=?\]
\[{{t}_{1}}=\frac{{{s}_{1}}}{{{u}_{1}}}=\frac{200}{10}=20s\]
\[BO\]
\[{{s}_{2}}=100m\]
\[{{u}_{2}}=0\]
\[{{a}_{2}}=2m/{{s}_{2}}\]
\[{{t}_{2}}=?\]
\[{{s}_{2}}={{u}_{2}}{{t}_{2}}+\frac{1}{2}{{a}_{2}}{{t}_{2}}\Rightarrow 100=\frac{1}{2}\times 2\times t_{2}^{2}\]
\[\Rightarrow {{t}_{2}}=10\sec \]
\[\therefore \Delta t={{t}_{1}}-{{t}_{2}}=20-10=10\sec .\]
The interval between the moments when the cars pass the intersection is 10 sec.
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