A car travelling at $60 \mathrm{~km} / \mathrm{h}$ overtakes another car travelling at $42 \mathrm{~km} / \mathrm{h}$. Assuming each car to be $5.0 \mathrm{~m}$ long, find the time taken during the overtake and the total road distance used for the overtake.
$\vec{V}_{1}=60^{\times \frac{5}{18}}=16.6 \mathrm{~m} / \mathrm{s}$
$\vec{V}_{2}=42^{\times \frac{2}{18}}=11.6 \mathrm{~m} / \mathrm{s}$
Relative velocity $=16.6-11.6$
$V_{\text {rel }}=5 \mathrm{~m} / \mathrm{s}$
$\mathrm{d}_{\mathrm{res}}=10 \mathrm{~m}$
Time to cross $=\frac{\mathrm{d}_{\mathrm{rel}}}{\mathrm{v}_{\mathrm{rel}}}=\frac{10}{5}=2 \mathrm{sec}$
In $2 \mathrm{sec}, 1^{\text {st }}$ car moves $=16.6 \times 2$ $=33.2$
Length of road $=33.2+$ length of car $=33.2+5$
$\approx 38 \mathrm{~m}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.